Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17753 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C42×C19 ◁ G | |
1020 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)(20,21,24,26,25,22,23,27)(28,29,32,36,33,37,31,35)(30,38,39,43,40,34,41,42);(20,22)(21,25)(23,27)(24,26)(28,30)(29,34)(31,39)(32,41)(33,40)(35,42)(36,43)(37,38);(20,23,25,24)(21,26,22,27)(28,31,33,32)(29,35,37,36)(30,39,40,41)(34,42,38,43);(28,31,33,32)(29,36,37,35)(30,39,40,41)(34,43,38,42)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10741);