Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19575 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
568 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)(20,21,25,28)(22,29,31,34)(23,27,24,33)(26,32,35,30)(36,37,41,45)(38,42,47,56)(39,49,51,59)(40,52,54,44)(43,53,58,50)(46,60,61,67)(48,64,63,57)(55,65,66,62);(20,22,24,30,25,31,23,32)(21,26,27,29,28,35,33,34)(36,38)(37,42)(39,46)(40,48)(41,47)(43,55)(44,57)(45,56)(49,60)(50,62)(51,61)(52,64)(53,65)(54,63)(58,66)(59,67);(20,21)(22,26)(23,33)(24,27)(25,28)(29,30)(31,35)(32,34)(36,39,41,51)(37,43,45,58)(38,46,47,61)(40,53,54,50)(42,55,56,66)(44,59,52,49)(48,65,63,62)(57,67,64,60);(20,23,25,24)(21,27,28,33)(22,30,31,32)(26,34,35,29)(38,47)(42,56)(46,61)(48,63)(55,66)(57,64)(60,67)(62,65)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12563);