Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19059 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(21,26)(22,29)(23,24)(28,31)(30,32)(33,35)(37,41)(39,46)(42,50)(43,47)(45,48)(49,51);(20,21)(22,27)(23,31)(24,26)(25,28)(29,35)(30,34)(32,33)(36,37,40,43)(38,42,44,51)(39,47,46,41)(45,49,48,50);(20,22)(21,27)(23,29)(24,32)(25,30)(26,33)(28,34)(31,35)(36,38)(37,42)(39,48)(40,44)(41,49)(43,51)(45,46)(47,50);(22,30)(27,34)(29,32)(33,35)(38,44)(42,51)(45,48)(49,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12047);