Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#13151 |
| 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 | C2×#135×C59 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×C8×C59 ◁ C2×C4×C8×C59 ◁ G | |
332 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)(5,6,10,17,12,18,11,27)(7,19,22,30,24,35,23,33)(8,16,25,29,26,34,9,15)(13,28,31,36,32,21,14,20)(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);(5,7,8,20,10,22,25,28,12,24,26,36,11,23,9,21)(6,13,29,35,27,14,16,30,18,32,15,19,17,31,34,33);(2,4)(5,7,8,20,10,22,25,28,12,24,26,36,11,23,9,21)(6,14,15,33,27,32,34,35,18,31,29,30,17,13,16,19)4484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6139);