Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18984 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
990 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)(21,24)(22,26)(25,27)(28,29)(30,38)(31,40)(32,35)(33,36)(34,37)(39,42)(41,43);(22,26)(24,27)(28,30)(29,31)(32,39)(33,40)(34,41)(35,38)(36,43)(37,42);(20,21)(22,27)(23,25)(24,26)(28,31)(29,30)(32,38)(33,43)(34,42)(35,39)(36,40)(37,41);(28,32,34,33)(29,35,37,36)(30,39,41,40)(31,38,42,43)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11972);