Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19071 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3553 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
810 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)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37,42,47)(38,48,51,60)(39,52,53,61)(40,46,41,45)(43,55,58,50)(44,56,59,54)(49,57,63,67)(62,64,66,65);(20,21)(22,26)(23,27)(24,32)(25,28)(29,33)(30,34)(31,35)(36,38)(37,43)(39,49)(40,55)(41,50)(42,51)(44,57)(45,60)(46,48)(47,58)(52,66)(53,63)(54,65)(56,64)(59,67)(61,62);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,39,42,53)(37,44,47,59)(38,49,51,63)(40,54,41,56)(43,57,58,67)(45,52,46,61)(48,62,60,66)(50,64,55,65);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(39,53)(44,59)(49,63)(52,61)(54,56)(57,67)(62,66)(64,65)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12059);