Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#21911 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C24 |
| commutator | C23 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C23×C59 | C23×C4 |
| prime radical | C22×#41×C59 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,13)(12,14)(15,16)(17,18,21,25,20,24,28,32)(19,23,27,31,26,22,29,30)(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)(2,5)(4,8)(6,7)(9,11,12,15)(10,13,14,16)(17,19)(18,22)(20,26)(21,27)(23,24)(25,30)(28,29)(31,32);(3,8)(5,7)(10,14)(13,16)(17,19)(18,23)(20,26)(21,27)(22,24)(25,31)(28,29)(30,32);(2,6)(5,7)(18,24)(19,26)(25,32)(27,29)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 14899);