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×#10606 |
| 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)(20,21,22,27,24,23,25,26)(28,29)(30,38)(31,36)(32,35)(33,37)(34,40)(39,42)(41,43);(20,22,24,25)(21,26,23,27)(28,30,31,40,33,39,32,41)(29,34,35,38,37,43,36,42);(20,23,24,21)(22,27,25,26)(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, 3594);