Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19092 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3219 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
816 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)(21,26)(22,29)(23,24)(28,31)(30,32)(33,35)(36,37)(38,46)(39,43)(40,52)(41,44)(42,49)(45,55)(47,63)(48,60)(50,61)(51,58)(53,57)(54,59)(56,65)(62,64)(66,67);(20,21)(22,27)(23,31)(24,26)(25,28)(29,35)(30,34)(32,33)(36,38,41,48)(37,42,44,57)(39,47,51,64)(40,53,55,49)(43,56,58,67)(45,60,52,46)(50,66,54,65)(59,62,61,63);(20,22,25,30)(21,27,28,34)(23,29,24,32)(26,33,31,35)(36,39,41,51)(37,43,44,58)(38,47,48,64)(40,54,55,50)(42,56,57,67)(45,61,52,59)(46,62,60,63)(49,66,53,65);(21,28)(26,31)(27,34)(33,35)(37,44)(38,48)(43,58)(45,52)(47,64)(49,53)(59,61)(65,66)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12080);