Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10500 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10503 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(22,27)(23,24)(28,29)(30,33)(31,34)(32,36)(35,40)(37,41)(38,43)(39,42);(20,21)(22,23)(24,26)(25,27)(28,30,32,38)(29,33,36,43)(31,39,40,37)(34,42,35,41);(20,22,23,21,25,26,24,27)(29,34)(31,40)(33,41)(35,36)(37,39)(42,43)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3491);