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×#26192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
734 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)(23,27)(24,26)(28,29)(30,40)(31,46)(32,49)(33,39)(34,38)(35,43)(36,48)(37,47)(41,54)(42,52)(44,56)(45,53)(50,55)(51,59)(57,58);(20,22,24,23)(21,25,26,27)(28,30,33,44)(29,35,39,53)(31,42,48,59)(32,45,34,43)(36,54,46,57)(37,52,55,51)(38,56,49,40)(41,50,58,47);(20,23,24,22)(21,25,26,27)(28,31)(29,36)(30,41)(32,47)(33,48)(34,50)(35,51)(37,38)(39,46)(40,57)(42,43)(44,58)(45,59)(49,55)(52,53)(54,56);(28,31)(29,37)(30,42)(32,50)(33,48)(34,47)(35,52)(36,38)(39,55)(40,57)(41,43)(44,59)(45,58)(46,49)(51,53)(54,56)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19180);