Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7262 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#7279 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #340 |
| commutator | C2×C8 | C42×C19 |
| Frattini, cosocle | C2×C4×C8 | C22×C19 |
| prime radical | C23×C19 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 2 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,24)(23,26)(25,27)(28,29)(30,40,42,54)(31,37)(32,47)(33,49)(34,39)(35,41,50,55)(36,45)(38,48)(43,58,56,52)(44,59,57,51)(46,53);(21,24)(22,27)(25,26)(28,30,32,43,48,57,46,55,34,42,45,56,33,44,31,41)(29,35,37,51,49,58,36,40,39,50,53,59,38,52,47,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 267);