Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18468 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3559 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
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)(22,26)(23,25)(24,27)(28,31)(29,34)(30,32)(33,35)(36,37,41,45)(38,42,48,55)(39,43,50,57)(40,51,52,44)(46,58,60,53)(47,61,62,54)(49,63,64,56)(59,65,67,66);(21,25)(23,31)(26,32)(27,28)(30,35)(33,34)(36,38)(37,42)(39,46)(40,47)(41,48)(43,53)(44,54)(45,55)(49,59)(50,60)(51,61)(52,62)(56,65)(57,58)(63,66)(64,67);(20,22,24,29)(21,26,27,34)(23,30,31,35)(25,32,28,33)(36,39)(37,43)(38,46)(40,49)(41,50)(42,53)(44,56)(45,57)(47,59)(48,60)(51,63)(52,64)(54,65)(55,58)(61,66)(62,67);(21,27)(22,29)(25,28)(30,35)(36,40,41,52)(37,44,45,51)(38,47,48,62)(39,49,50,64)(42,54,55,61)(43,56,57,63)(46,59,60,67)(53,65,58,66)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11456);