Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3531 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
820 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)(36,37,42,47)(38,48,52,58)(39,53,55,61)(40,46,41,45)(43,50,59,51)(44,56,60,54)(49,57,65,67)(62,64,66,63);(20,21,24,27)(22,25,29,34)(23,31,30,26)(28,35,32,33)(36,38)(37,43)(39,49)(40,50)(41,51)(42,52)(44,57)(45,58)(46,48)(47,59)(53,66)(54,63)(55,65)(56,64)(60,67)(61,62);(20,22)(21,25)(23,32)(24,29)(26,35)(27,34)(28,30)(31,33)(36,39)(37,44)(38,49)(40,54)(41,56)(42,55)(43,57)(45,53)(46,61)(47,60)(48,62)(50,63)(51,64)(52,65)(58,66)(59,67);(36,40,42,41)(37,45,47,46)(38,50,52,51)(39,54,55,56)(43,58,59,48)(44,53,60,61)(49,63,65,64)(57,66,67,62)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11993);