Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#24930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
862 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)(22,24)(23,25)(26,27)(28,29)(30,39)(31,44)(32,34)(33,38)(35,43)(36,45)(37,48)(40,49)(41,56)(42,51)(46,53)(47,52)(50,58)(54,55)(57,59);(20,22,23,26)(21,24,25,27)(29,34)(30,40)(32,48)(36,44)(37,38)(41,55)(42,43)(45,47)(49,51)(52,53)(56,59)(57,58);(21,25)(24,27)(28,30)(29,35)(31,41)(32,42)(33,43)(34,49)(36,50)(37,51)(38,39)(40,48)(44,59)(45,55)(46,57)(47,58)(52,54)(53,56);(28,31,33,46)(29,36,38,52)(30,41,43,57)(32,47,48,45)(34,44,37,53)(35,50,39,54)(40,55,42,58)(49,59,51,56)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17918);