Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33803 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
456 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)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37,42,46)(38,47,48,64)(39,44,41,56)(40,52,55,66)(43,58,59,50)(45,51,63,54)(49,65,57,62)(53,60,67,61);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(38,48)(43,59)(47,64)(49,57)(50,58)(53,67)(60,61)(62,65);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,38)(37,43)(39,49)(40,53)(41,57)(42,48)(44,60)(45,62)(46,59)(47,52)(50,54)(51,58)(55,67)(56,61)(63,65)(64,66);(21,27)(25,28)(26,35)(33,34)(36,39,42,41)(37,44,46,56)(38,49,48,57)(40,51,55,54)(43,60,59,61)(45,52,63,66)(47,65,64,62)(50,53,58,67)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26791);