Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20348 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C4 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×#41×C19 ◁ G | |
2158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 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)(22,23)(24,25,26,27)(29,34)(31,32)(35,41)(36,37)(39,40)(42,43);(21,23)(28,29,32,36,33,37,31,34)(30,35,40,43,38,42,39,41);(28,30)(29,35)(31,39)(32,40)(33,38)(34,41)(36,43)(37,42);(30,38)(35,42)(39,40)(41,43)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13336);