Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#16194 |
| 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 | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(28,29)(30,33)(31,32)(34,35)(36,37,39,40)(38,42,43,41)(45,48)(49,50);(29,32)(30,34)(37,40)(41,42)(44,45,47,48)(46,50,51,49);(20,21)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)(36,38,39,43)(37,41,40,42)(44,45)(46,49)(47,48)(50,51);(20,22,23,26)(21,25,24,27)(28,30,31,34)(29,33,32,35)(36,37)(38,41)(39,40)(42,43)(44,46)(45,49)(47,51)(48,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 9182);