Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11356 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #390 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C2×C59 | #1445 |
| prime radical | C24×C59 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2)(3,11)(4,15,17,8)(5,18)(6,10)(7,13)(9,20)(12,26,28,32)(14,25)(16,24,31,29)(19,22)(21,30,23,27)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,5,19,6,14,20,13)(2,7,18,11,10,22,9,25)(4,12,16,30,17,28,31,27)(8,23,29,32,15,21,24,26);(1,4,5,16,6,17,20,31)(2,8,18,29,10,15,9,24)(3,12,19,30,14,28,13,27)(7,21,11,26,22,23,25,32)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4344);