Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23989 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1210 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)(22,26)(23,25)(24,27)(28,29)(30,34)(31,35)(32,36)(33,37)(38,48)(39,46)(40,47)(41,49)(42,50)(43,51)(44,52)(45,54)(53,58)(55,57)(56,59);(20,22,23,27)(21,24,25,26)(28,30)(29,34)(31,38)(32,39)(33,40)(35,48)(36,46)(37,47)(41,53)(42,54)(43,55)(44,56)(45,50)(49,58)(51,57)(52,59);(28,31,33,42)(29,35,37,50)(30,38,40,54)(32,43,44,41)(34,45,47,48)(36,51,52,49)(39,55,56,53)(46,58,59,57);(21,25)(24,26)(28,32,33,44)(29,36,37,52)(30,39,40,56)(31,41,42,43)(34,46,47,59)(35,49,50,51)(38,53,54,55)(45,57,48,58)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16977);