Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#13170 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C2×D8 |
| commutator | C2×C8 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C22×C59 | C4×D8 |
| prime radical | C23×C59 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×C8×C59 ◁ C2×C4×C8×C59 ◁ G | |
278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2)(3,4)(5,6,10,15,11,17,26,16)(7,12,9,25,19,14,27,29)(8,20,23,34,24,28,33,35)(13,21,30,36,32,18,31,22)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(2,4)(5,7,10,9,11,19,26,27)(6,12,15,25,17,14,16,29)(8,21,23,36,24,18,33,22)(13,20,30,34,32,28,31,35);(5,8,19,21,10,23,27,36,11,24,7,18,26,33,9,22)(6,13,25,35,16,31,12,28,17,32,29,34,15,30,14,20)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6158);