Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#10610 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #396 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | C22⋊Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
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)(20,21,24,27,23,26,22,25)(28,29,33,37)(30,38,39,42)(31,36,32,35)(34,41,43,40);(28,30,31,40,33,39,32,41)(29,34,35,38,37,43,36,42);(20,21,23,26)(22,27,24,25)(29,35)(30,39)(31,32)(34,38)(36,37)(42,43)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3598);