Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9159 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#9182 |
| 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 | |
500 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)(20,21,25,26,24,22,23,27)(28,29,32,35)(30,33)(31,36,40,41)(34,39)(37,43)(38,42);(20,22,24,21)(23,27,25,26)(28,30)(29,33,35,43)(31,39)(32,37)(34,41,42,36)(38,40);(20,23,24,25)(21,26,22,27)(28,30)(29,34)(31,39)(32,37)(33,41)(35,42)(36,43)(38,40)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2170);