Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#15517 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4864 |
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)(21,23)(24,25)(26,27)(28,29,31,33)(30,32,34,35)(37,38)(39,43);(25,26)(30,34)(32,35)(36,37,40,38)(39,42,43,41);(28,30)(29,32)(31,34)(33,35)(36,38,40,37)(39,42,43,41);(20,21)(22,23)(24,26,27,25)(28,29)(30,32)(31,33)(34,35)(36,39,40,43)(37,41,38,42)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 8505);