Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#11855 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
324 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(22,28,30,25)(23,26)(24,27)(29,34,31,33)(32,35)(36,37)(38,48)(39,45)(40,55)(41,58)(42,47)(43,50)(44,53)(46,57)(49,61)(51,67)(52,63)(54,64)(56,65)(59,60)(62,66);(20,22)(21,25)(23,31)(24,30)(26,34)(27,28)(29,32)(33,35)(36,38)(37,43)(39,50)(40,56)(41,59)(42,52)(44,63)(45,60)(46,65)(47,62)(48,55)(49,53)(51,57)(54,66)(58,61)(64,67);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,39,41,53,42,54,57,40)(37,44,46,45,47,55,58,64)(38,49,51,50,52,56,59,66)(43,60,61,63,62,67,65,48)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4843);