Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3559 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
892 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)(22,29)(23,24)(28,31)(30,32)(33,35)(36,37,41,39)(38,44,46,51)(40,48,50,43)(42,49,45,47);(20,21)(22,27)(23,31)(24,26)(25,28)(29,35)(30,34)(32,33)(36,38)(37,42)(39,45)(40,49)(41,46)(43,51)(44,48)(47,50);(20,22,25,30)(21,27,28,34)(23,29,24,32)(26,33,31,35)(36,39,41,37)(38,45,46,42)(40,43,50,48)(44,49,51,47);(21,28)(26,31)(27,34)(33,35)(38,46)(42,45)(44,51)(47,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12010);