Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19012 |
| 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 | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(23,24)(27,34)(28,31)(29,32)(33,35)(36,37)(38,45)(39,43)(40,48)(41,44)(42,46)(47,50)(49,51);(20,21,25,28)(22,27,30,35)(23,26,24,31)(29,33,32,34)(36,37)(38,42)(39,43)(40,48)(41,44)(45,49)(46,50)(47,51);(20,22)(21,27)(23,29)(24,32)(25,30)(26,33)(28,35)(31,34)(36,38)(37,42)(39,46)(40,49)(41,47)(43,50)(44,51)(45,48);(20,23,25,24)(21,26,28,31)(22,29,30,32)(27,33,35,34)(36,39,41,40)(37,43,44,48)(38,46,47,49)(42,50,51,45)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12000);