Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23560 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1082 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 608 |
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)(22,27,23,25)(28,29)(30,34)(31,36)(32,40)(33,37)(35,38)(39,43)(41,42);(20,22,24,23)(21,25,26,27)(28,30)(29,34)(31,38)(32,41)(33,39)(35,36)(37,43)(40,42);(20,23,24,22)(21,25,26,27)(28,30)(29,35)(31,38)(32,41)(33,39)(34,40)(36,43)(37,42);(28,31,33,32)(29,36,37,40)(30,38,39,41)(34,35,43,42)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16548);