Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8504 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #379 |
| prime radical | C19×#3529 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24,25,26)(28,29)(30,38,41,34)(31,42,43,53)(32,37)(33,36)(35,44,50,46)(39,55)(40,52,45,49)(47,51)(48,57)(54,58)(56,59);(20,21)(22,26)(23,25)(24,27)(28,30)(29,34)(31,39)(32,45)(33,41)(35,48)(36,38)(37,52)(40,47)(42,55)(43,56)(44,58)(46,57)(49,51)(50,54)(53,59);(22,27)(24,26)(28,31)(29,35)(30,39)(32,46)(33,43)(34,48)(36,50)(37,53)(38,54)(40,58)(41,56)(42,51)(44,47)(45,57)(49,55)(52,59)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1492);