Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#7180 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C59 | #106 |
| commutator | C8 | C4×C8×C59 |
| Frattini, cosocle | C2×C4×C8 | C22×C59 |
| socle | C2×C59 | #1279 |
| prime radical | C23×C59 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C59 ◁ C22×C8×C59 ◁ C2×C4×C8×C59 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 2 generators on 91 points:
(1,2,5,11,7,13,23,28,8,14,22,10,6,12,4,21)(3,15,17,26,19,31,16,27,20,29,24,25,18,30,32,9)(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)(2,9,12,25,14,27,13,26)(4,16)(5,24)(6,18)(7,19)(8,20)(10,15,28,30,11,29,21,31)(17,22)(23,32)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 168);