Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#22304 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C24 |
| commutator | C23 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle, prime radical | C23×C59 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,5)(3,7)(9,10)(11,14)(12,16)(13,15)(17,18,23,19,22,26,21,25)(20,24,28,27,29,31,30,32)(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);(1,2)(3,6)(4,5)(7,8)(9,11,13,12)(10,14,15,16)(17,19,23,26,22,25,21,18)(20,27,28,31,29,32,30,24);(2,5)(6,8)(9,12,13,11)(10,14,15,16)(17,20)(18,24)(19,27)(21,30)(22,29)(23,28)(25,32)(26,31);(1,3,4,7)(2,6,5,8)(17,21,22,23)(18,25,26,19)(20,28,29,30)(24,27,31,32)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 15292);