Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33630 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(20,21,23,25)(22,26,27,24)(28,29,32,35)(30,40,42,57)(31,39,34,37)(33,46,45,54)(36,52,50,43)(38,44,51,48)(41,58,49,55)(47,56,59,53);(20,22,23,27)(21,24,25,26)(29,35)(36,50)(37,39)(38,51)(40,57)(46,54)(53,56)(55,58);(28,30)(29,36)(31,41)(32,42)(33,47)(34,49)(35,50)(37,53)(38,55)(39,56)(40,46)(43,48)(44,52)(45,59)(51,58)(54,57);(28,31,32,34)(29,37,35,39)(30,41,42,49)(33,44,45,48)(36,53,50,56)(38,54,51,46)(40,55,57,58)(43,47,52,59)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26618);