Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#18230 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3002 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
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)(24,27)(28,29)(30,37)(31,34)(32,36)(33,41)(35,39)(38,42)(40,43);(20,21)(22,24)(23,25)(26,27)(28,30)(29,35)(31,38)(32,39)(33,42)(34,40)(36,43)(37,41);(20,22)(21,24)(23,26)(25,27)(28,31,34,29)(30,38,40,35)(32,36,33,41)(37,39,43,42);(28,32,34,33)(29,36,31,41)(30,39,40,42)(35,43,38,37)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11218);