Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#33706 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(22,25)(23,24)(26,27)(28,29)(30,42)(31,36)(32,50)(33,53)(34,54)(35,41)(37,44)(38,43)(39,52)(40,51)(45,57)(46,56)(47,55)(48,59)(49,58);(21,24)(25,27)(28,30,43,49,34,46,52,47,35,44,33,45,51,48,32,31)(29,36,50,59,40,57,53,37,41,55,39,56,54,58,38,42);(20,22,23,26)(21,25,24,27)(28,31,32,48,51,45,33,44,35,47,52,46,34,49,43,30)(29,37,38,57,54,59,39,36,41,42,53,58,40,56,50,55);(30,44)(31,47)(36,55)(37,42)(45,49)(46,48)(56,59)(57,58)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26694);