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×#33806 |
| 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 | |
462 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)(38,48)(39,47)(40,43)(41,54)(42,45)(44,51)(46,56)(49,65)(50,64)(52,59)(53,61)(55,63)(57,62)(58,66)(60,67);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(37,43)(44,58)(45,47)(46,59)(48,64)(54,61)(60,63)(62,65);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,38,40,50)(37,44,43,58)(39,49,42,57)(41,55,53,67)(45,60,47,63)(46,62,59,65)(48,61,64,54)(51,52,66,56);(21,27)(25,28)(26,35)(33,34)(36,39,40,42)(37,45,43,47)(38,49,50,57)(41,52,53,56)(44,60,58,63)(46,61,59,54)(48,62,64,65)(51,55,66,67)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26794);