Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3115 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
872 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)(20,21)(22,29)(23,27)(24,33)(25,28)(26,30)(31,35)(32,34)(37,42)(38,46)(39,40)(44,45)(47,48)(49,50);(20,22)(21,26)(23,30)(24,31)(25,32)(27,34)(28,35)(29,33)(36,37,41,45)(38,43,47,51)(39,42,40,44)(46,49,48,50);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,34,35,29)(36,38,41,47)(37,43,45,51)(39,46,40,48)(42,49,44,50);(20,23,25,24)(21,27,28,33)(22,31,32,30)(26,29,35,34)(36,39,41,40)(37,44,45,42)(38,46,47,48)(43,50,51,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11818);