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×#33798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
468 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)(38,42)(39,43)(40,53)(41,46)(44,50)(45,51)(47,54)(48,63)(49,57)(52,59)(55,60)(56,61)(58,64)(62,66)(65,67);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38,41,49)(37,42,46,57)(39,47,52,62)(40,48,51,61)(43,54,59,66)(44,55,58,65)(45,56,53,63)(50,60,64,67);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(37,43)(39,50)(40,51)(42,54)(44,45)(46,59)(47,60)(48,61)(52,64)(53,58)(55,56)(57,66)(62,67)(63,65);(21,27)(25,28)(26,35)(33,34)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26786);