Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9307 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#9310 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(30,34,39,50)(31,41)(32,45)(33,36)(35,43)(37,47)(38,54,42,59)(40,57,56,49)(44,53)(46,52)(48,58,51,55);(20,21,22,27,24,26,23,25)(28,30,33,39)(29,34)(31,42,44,38)(32,40,47,56)(35,51)(36,50)(37,49)(41,59)(43,58,46,55)(45,57)(48,52)(53,54);(20,22,24,23)(21,25,26,27)(28,31,33,44)(29,35,36,52)(30,38,39,42)(32,46,47,43)(34,48,50,51)(37,53,45,41)(40,58,56,55)(49,59,57,54)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2298);