A146074 -id:A146074

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A145665

a(n) = number of elements of order n in simple group M_11 of order 7920.

+10
4

1, 165, 440, 990, 1584, 1320, 0, 1980, 0, 0, 1440

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].

LINKS

Table of n, a(n) for n=1..11.

ATLAS, Mathieu group M11

PROG

(Magma) /* Mathieu group M11 presented on its standard generators. */

G<x, y>:=Group<x, y|x^2, y^4, (x*y)^11, (x*y^2)^6, x*y*x*y*x*y^-1*x*y*x*y^2*x*y^-1*x*y*x*y^-1*x*y^-1>;

H:= sub< G | x>;

f, L := CosetAction(G, H);

// Order(G) eq Order(L); /* 7920 = 7920*/

t2:=Classes(L);

t1:=[0 : n in [1..11]];

for c in t2 do t1[c[1]] := t1[c[1]] + c[2]; end for;

t1; /* edited by Charles R Greathouse IV, May 29 2015 */

CROSSREFS

Cf. A284842 (M_12), A284846 (M_22), A284872 (M_23), A146074 (M_24).

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane, Apr 06 2009

STATUS

approved

A284842

Number of elements of order n in simple Mathieu group M_12.

+10
4

1, 891, 4400, 5940, 9504, 23760, 0, 23760, 0, 9504, 17280

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

LINKS

Table of n, a(n) for n=1..11.

ATLAS, Mathieu group 12.

CROSSREFS

Cf. A145665 (M_11), A284846 (M_22), A284872 (M_23), A146074 (M_24).

KEYWORD

nonn,fini,full

AUTHOR

Sean A. Irvine, Apr 03 2017

STATUS

approved

A284846

Number of elements of order n in simple Mathieu group M_22

+10
4

1, 1155, 12320, 41580, 88704, 36960, 126720, 55440, 0, 0, 80640

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

LINKS

Table of n, a(n) for n=1..11.

ATLAS, Mathieu group 22

CROSSREFS

Cf. A145665 (M_11), A284842 (M_12), A284872 (M_23), A146074 (M_24).

KEYWORD

nonn,fini,full

AUTHOR

Sean A. Irvine, Apr 03 2017

STATUS

approved

A284872

Number of elements of order n in simple Mathieu group M_23.

+10
4

1, 3795, 56672, 318780, 680064, 850080, 1457280, 1275120, 0, 0, 1854720, 0, 0, 1457280, 1360128, 0, 0, 0, 0, 0, 0, 0, 887040

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

ATLAS, Mathieu group 23

CROSSREFS

Cf. A145665 (M_11), A284842 (M_12), A284846 (M_22), A146074 (M_24).

KEYWORD

nonn,fini,full

AUTHOR

Sean A. Irvine, Apr 04 2017

STATUS

approved

A028825

List of sizes of conjugacy classes of Mathieu simple group M_24 of order 244823040.

+10
2

1, 2, 2, 3, 3, 4, 4, 4, 5, 6, 6, 7, 7, 8, 10, 11, 12, 12, 14, 14, 15, 15, 21, 21, 23, 23

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Equally, list of orders of elements of Mathieu group M_24.

REFERENCES

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups, Oxford Univ. Press, 1985.

LINKS

Table of n, a(n) for n=1..26.

ATLAS, Mathieu group M24

EXAMPLE

The conjugacy classes and the orders of their centralizers are:

1A 244823040

2A 21504

2B 7680

3A 1080

3B 504

4A 384

4B 128

4C 96

5A 60

6A 24

6B 24

7A 42

7B 42

8A 16

10A 20

11A 11

12A 12

12B 12

14A 14

14B 14

15A 15

15B 15

21A 21

21B 21

23A 23

23B 23

CROSSREFS

Cf. A146073, A146074.

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane. Entry revised Apr 07 2009

STATUS

approved

A146073

List of orders of centralizers of conjugacy classes of Mathieu simple group M_24 of order 244823040.

+10
2

244823040, 21504, 7680, 1080, 504, 384, 128, 96, 60, 24, 24, 42, 42, 16, 20, 11, 12, 12, 14, 14, 15, 15, 21, 21, 23, 23

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups, Oxford Univ. Press, 1985.

LINKS

Table of n, a(n) for n=1..26.

ATLAS, Mathieu group M24

CROSSREFS

Cf. A028825, A146074.

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane, Apr 07 2009

STATUS

approved

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