Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
808 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(22,28)(23,30)(25,33)(26,31)(29,32)(34,35)(36,37)(38,48)(39,52)(40,47)(41,46)(42,45)(43,50)(44,53)(49,57)(51,60)(54,61)(55,58)(56,59)(62,64)(63,66)(65,67);(20,21,24,27)(22,25,29,34)(23,31,30,26)(28,35,32,33)(36,38)(37,43)(39,49)(40,55)(41,50)(42,51)(44,57)(45,58)(46,60)(47,48)(52,66)(53,64)(54,65)(56,63)(59,67)(61,62);(20,22)(21,25)(23,32)(24,29)(26,35)(27,34)(28,30)(31,33)(36,39,42,54)(37,44,45,59)(38,49,51,65)(40,53,41,56)(43,57,58,67)(46,52,47,61)(48,62,60,66)(50,63,55,64);(37,45)(43,58)(44,59)(46,47)(48,60)(52,61)(57,67)(62,66)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11991);