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×#26193 |
| 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)(30,41)(31,36)(32,49)(33,39)(34,40)(35,44)(37,48)(38,51)(42,55)(43,52)(45,53)(46,59)(47,56)(50,54)(57,58);(20,22,24,23)(21,25,26,27)(28,30)(29,35)(31,46)(32,43)(33,50)(34,45)(36,55)(37,52)(38,53)(39,41)(40,54)(42,48)(44,51)(47,58)(49,57)(56,59);(20,23,24,22)(21,25,26,27)(28,31,34,32)(29,36,40,49)(30,42,45,58)(33,47,51,48)(35,52,54,59)(37,39,56,38)(41,55,53,57)(43,50,46,44);(28,32,34,31)(29,37,40,56)(30,43,45,46)(33,47,51,48)(35,52,54,59)(36,39,49,38)(41,57,53,55)(42,50,58,44)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19181);