Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7537 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D32 |
| commutator | C32 | C2×C4×C19 |
| Frattini, cosocle | C2×C32 | C22×C19 |
| prime radical | C2×C19×D32 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×C19 ◁ C2×C8×C19 ◁ C2×C16×C19 ◁ C2×C19×C32 ◁ G | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 2 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,31)(27,42)(28,46)(29,49)(30,36)(32,37)(33,38)(34,43)(35,47)(39,59)(40,61)(41,53)(44,77)(45,75)(48,79)(50,63)(51,62)(52,70)(54,69)(55,72)(56,65)(57,78)(58,68)(60,76)(64,80)(66,74)(67,73)(71,84)(81,87)(82,86)(83,85);(25,31)(26,37)(27,38)(28,43)(29,47)(32,33)(34,59)(35,61)(36,53)(39,69)(40,72)(41,65)(42,50)(44,78)(45,68)(46,51)(48,76)(49,52)(54,74)(55,73)(56,58)(57,80)(60,84)(62,63)(64,70)(66,67)(71,87)(75,82)(77,81)(79,83)(85,86)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 525);