Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#29194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C22×D4×C59 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C43×C59 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,4,5)(3,7,8,6)(9,10,12,14)(11,13,15,16)(17,18,20,22)(19,25,26,32)(21,29,28,24)(23,31,30,27)(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);(2,5)(6,7)(9,11,12,15)(10,13,14,16)(18,22)(23,30)(24,29)(25,32);(11,15)(13,16)(17,19,21,27,20,26,28,31)(18,23,24,25,22,30,29,32);(1,3,4,8)(2,6,5,7)(18,22)(23,30)(24,29)(25,32)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 22182);