Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#33468 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #442 |
| commutator | C8 | C23×C4×C59 |
| Frattini, cosocle | C2×C8 | C24×C59 |
| socle | C2×C59 | C2×#442 |
| prime radical | C59×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×C4×C59 ◁ C2×#97×C59 ◁ G | |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,14,17,24)(4,18)(5,11)(6,10)(7,22)(8,13)(9,15,26,32)(12,20)(16,29,23,30)(19,28)(21,25,31,27)(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)(2,9)(4,15)(5,16)(6,21)(7,23)(8,17)(10,24)(11,25)(12,29)(13,26)(14,28)(18,30)(19,31)(20,32)(22,27);(1,4,7,6,8,20,5,19)(2,10,11,18,13,28,22,12)(3,15,23,21,17,32,16,31)(9,24,25,30,26,14,27,29);(1,5,8,7)(2,11,13,22)(3,16,17,23)(4,19,20,6)(9,25,26,27)(10,18,28,12)(14,29,24,30)(15,31,32,21)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26456);