Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C26×C4 |
| direct product | C19×#36818 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2056 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)(21,23)(22,26)(30,34)(33,35)(37,41)(38,39);(20,21,24,23)(22,27,26,25)(29,32)(33,35)(36,37,40,41)(38,42,39,43);(28,29)(30,33)(31,32)(34,35)(36,38,40,39)(37,42,41,43);(20,22,24,26)(21,25,23,27)(28,29)(30,33)(31,32)(34,35)(36,37)(38,42)(39,43)(40,41);(20,23,24,21)(22,27,26,25)(28,30)(29,33)(31,34)(32,35)(36,39,40,38)(37,43,41,42)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29806);