Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18969 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30)(23,28)(24,27)(25,29)(26,32)(31,35)(33,34)(36,37,41,45)(38,46,49,59)(39,43,50,57)(40,52,54,44)(42,53,56,48)(47,60,61,67)(51,64,63,58)(55,65,66,62);(20,22,25,33)(21,26,29,35)(23,31,24,32)(27,34,28,30)(36,38,41,49)(37,42,45,56)(39,47,50,61)(40,53,54,48)(43,55,57,66)(44,59,52,46)(51,65,63,62)(58,67,64,60);(21,27)(23,24)(26,34)(28,29)(30,35)(31,32)(36,39)(37,43)(38,47)(40,51)(41,50)(42,55)(44,58)(45,57)(46,60)(48,62)(49,61)(52,64)(53,65)(54,63)(56,66)(59,67);(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)(39,50)(43,57)(47,61)(51,63)(55,66)(58,64)(60,67)(62,65)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11957);