Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33742 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
508 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)(22,25)(23,24)(26,27)(30,38)(31,42)(32,43)(34,45)(36,51)(37,50)(39,44)(40,55)(41,54)(46,49)(47,56)(48,59)(52,53)(57,58);(21,24)(25,27)(28,29)(30,34)(31,36)(32,37)(33,35)(38,45)(39,46)(40,48)(41,47)(42,51)(43,50)(44,49)(52,57)(53,58)(54,56)(55,59);(28,30,39,55,32,40,31,38,33,41,42,53,43,52,44,54)(29,34,46,59,37,48,36,45,35,47,51,58,50,57,49,56);(20,22,23,26)(21,25,24,27)(29,35)(34,47)(36,49)(37,50)(45,56)(46,51)(48,57)(58,59)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26730);