Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36734 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,24)(22,26,27,25)(30,34)(33,35)(38,42)(39,43);(21,24)(25,26)(29,32)(33,35)(36,37,40,41)(38,43,42,39);(28,29)(30,33)(31,32)(34,35)(36,38)(37,39)(40,42)(41,43);(20,21)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)(36,37)(38,39)(40,41)(42,43);(20,22,23,27)(21,25,24,26)(28,30)(29,33)(31,34)(32,35)(36,39)(37,38)(40,43)(41,42)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29722);