Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33797 |
| 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 | |
460 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)(38,47,50,65)(39,44,41,56)(40,52,55,66)(43,58,61,49)(45,51,63,54)(48,64,57,62)(53,59,67,60);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,38)(37,43)(39,48)(40,53)(41,57)(42,50)(44,59)(45,62)(46,61)(47,52)(49,54)(51,58)(55,67)(56,60)(63,64)(65,66);(21,27)(25,28)(26,35)(33,34)(36,39,42,41)(37,44,46,56)(38,48,50,57)(40,51,55,54)(43,59,61,60)(45,52,63,66)(47,64,65,62)(49,53,58,67)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26785);