Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1146 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)(20,21,23,25)(22,26,27,24)(28,29)(30,35)(31,42)(32,37)(33,46)(34,38)(36,44)(39,55)(40,49)(41,51)(43,53)(45,54)(47,50)(48,56)(52,58)(57,59);(20,22,23,27)(21,24,25,26)(28,30)(29,35)(31,39)(32,40)(33,47)(34,41)(36,52)(37,49)(38,51)(42,55)(43,56)(44,58)(45,57)(46,50)(48,53)(54,59);(28,31,34,45)(29,36,38,53)(30,39,41,57)(32,44,33,43)(35,48,51,52)(37,54,46,42)(40,58,47,56)(49,55,50,59);(28,32,34,33)(29,37,38,46)(30,40,41,47)(31,43,45,44)(35,49,51,50)(36,42,53,54)(39,56,57,58)(48,59,52,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16452);