Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33626 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C22×D8 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(28,29)(30,39)(31,36)(32,44)(33,48)(34,38)(35,41)(37,46)(40,55)(42,56)(43,54)(45,50)(47,58)(49,53)(51,59)(52,57);(20,22,23,27)(21,24,25,26);(28,30)(29,35)(31,40)(32,45)(33,49)(34,42)(36,50)(37,53)(38,52)(39,44)(41,46)(43,57)(47,59)(48,51)(54,55)(56,58);(28,31,34,33)(29,36,38,48)(30,40,42,49)(32,43,47,46)(35,50,52,51)(37,44,54,58)(39,55,56,53)(41,45,57,59)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26614);