Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(22,23)(26,27)(28,29,34,39)(30,35,42,51)(31,43,45,54)(32,38,33,37)(36,47,53,46)(40,52,56,59)(41,55,48,50)(44,49,57,58);(20,21,24,26)(22,25,23,27)(28,30)(29,35)(31,44)(32,41)(33,48)(34,42)(36,52)(37,50)(38,55)(39,51)(40,47)(43,58)(45,57)(46,56)(49,54)(53,59);(20,22,24,23)(21,25,26,27)(28,31)(29,36)(30,40)(32,47)(33,46)(34,45)(35,49)(37,54)(38,43)(39,53)(41,57)(42,56)(44,48)(50,59)(51,58)(52,55)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3175);