Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C23×C19 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
838 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
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)(24,33)(25,28)(26,31)(30,34)(32,35)(36,37,41,45)(38,42,48,55)(39,43,50,57)(40,51,52,44)(46,58,60,53)(47,61,62,54)(49,63,64,56)(59,65,67,66);(20,22,25,32)(21,26,28,34)(23,31,24,30)(27,35,33,29)(36,38)(37,42)(39,46)(40,47)(41,48)(43,53)(44,54)(45,55)(49,59)(50,60)(51,61)(52,62)(56,65)(57,58)(63,66)(64,67);(36,39,41,50)(37,43,45,57)(38,46,48,60)(40,49,52,64)(42,53,55,58)(44,56,51,63)(47,59,62,67)(54,65,61,66);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)(36,40,41,52)(37,44,45,51)(38,47,48,62)(39,49,50,64)(42,54,55,61)(43,56,57,63)(46,59,60,67)(53,65,58,66)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11362);