Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19046 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3180 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
836 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)(21,25)(23,30)(26,34)(27,31)(28,32)(33,35)(36,37)(38,45)(39,43)(40,48)(41,44)(42,46)(47,50)(49,51);(20,21)(22,26)(23,31)(24,27)(25,30)(28,33)(29,35)(32,34)(36,37)(38,42)(39,43)(40,48)(41,44)(45,49)(46,50)(47,51);(20,22,24,29)(21,26,27,35)(23,32,30,28)(25,33,31,34)(36,38)(37,42)(39,46)(40,49)(41,47)(43,50)(44,51)(45,48);(21,27)(25,31)(26,35)(33,34)(36,39,41,40)(37,43,44,48)(38,46,47,49)(42,50,51,45)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12034);