Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3486 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1214 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)(23,24)(26,27)(28,29)(30,34)(31,41)(32,44)(33,37)(35,43)(36,47)(38,55)(39,53)(40,50)(42,54)(45,49)(46,52)(48,57)(51,58)(56,59);(21,24)(25,27)(28,30,33,40)(29,34,37,50)(31,38,42,56)(32,45,47,39)(35,51,52,48)(36,53,44,49)(41,55,54,59)(43,58,46,57);(20,22,23,26)(21,25,24,27)(28,31)(29,35)(30,38)(32,46)(33,42)(34,48)(36,54)(37,52)(39,58)(40,56)(41,44)(43,47)(45,57)(49,59)(50,51)(53,55);(21,24)(25,27)(31,42)(35,52)(38,56)(41,54)(43,46)(48,51)(55,59)(57,58)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17011);