Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#11610 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C59 | C22⋊C4 |
| commutator | C2×C4 | C22×C8×C59 |
| Frattini, cosocle | C4×C8 | C23×C59 |
| socle | C22×C59 | C2×C22⋊C8 |
| prime radical | C23×C59 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C59 ◁ C2×C4×C8×C59 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 99 points:
(2,5)(3,7)(6,8)(9,10,12,17,14,18,25,32,13,16,24,29,26,30,37,39)(11,19,21,31,22,33,35,40,20,15,23,27,34,28,36,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2,4,6)(3,8,7,5)(9,11,13,20)(10,15,16,19)(12,23,24,21)(14,22,26,34)(17,31,29,27)(18,28,30,33)(25,36,37,35)(32,40,39,38);(11,20)(15,19)(21,23)(22,34)(27,31)(28,33)(35,36)(38,40)4484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4598);