Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19089 |
| 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 | |
850 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)(22,28)(23,31)(24,26)(25,30)(27,32)(29,35)(33,34)(36,37,42,47)(38,48,50,60)(39,52,54,61)(40,46,41,45)(43,55,58,51)(44,56,59,53)(49,57,63,67)(62,64,66,65);(23,32)(27,31)(28,35)(30,33)(36,38)(37,43)(39,49)(40,55)(41,51)(42,50)(44,57)(45,60)(46,48)(47,58)(52,66)(53,65)(54,63)(56,64)(59,67)(61,62);(20,22)(21,25)(23,33)(24,29)(26,34)(27,35)(28,31)(30,32)(36,39,42,54)(37,44,47,59)(38,49,50,63)(40,53,41,56)(43,57,58,67)(45,52,46,61)(48,62,60,66)(51,64,55,65);(21,26)(25,34)(27,31)(28,35)(38,50)(43,58)(48,60)(49,63)(51,55)(57,67)(62,66)(64,65)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12077);