Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18951 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C23×C19 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
790 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)(20,21,26,23)(22,29,32,35)(24,28,25,33)(27,34,30,31)(36,37)(38,42)(39,49)(40,52)(41,44)(43,51)(45,55)(46,62)(47,60)(48,57)(50,61)(53,58)(54,59)(56,64)(63,66)(65,67);(20,22)(21,27)(23,30)(24,31)(25,34)(26,32)(28,35)(29,33)(36,38,41,48)(37,42,44,57)(39,46,50,63)(40,53,55,47)(43,56,59,67)(45,60,52,58)(49,66,61,62)(51,65,54,64);(20,23,26,21)(22,30,32,27)(24,28,25,33)(29,31,35,34)(36,39)(37,43)(38,46)(40,54)(41,50)(42,56)(44,59)(45,61)(47,65)(48,63)(49,52)(51,55)(53,64)(57,67)(58,66)(60,62);(20,24,26,25)(21,28,23,33)(22,31,32,34)(27,35,30,29)(37,44)(42,57)(43,59)(45,52)(49,61)(56,67)(58,60)(62,66)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11939);