Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18123 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| prime radical | C19×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
1208 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)(20,21,23,26)(22,24,27,25)(33,39)(40,43);(21,24)(22,27)(25,26)(28,29)(30,33)(31,34)(32,35)(36,40)(37,39)(38,41)(42,43);(28,30)(29,33)(31,36)(32,37)(34,40)(35,39)(38,42)(41,43);(28,31,32,38)(29,34,35,41)(30,36,37,42)(33,40,39,43)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11111);