Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19651 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19668 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C23×C19 | #127 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
644 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)(24,33)(25,28)(26,31)(30,34)(32,35)(36,37,41,45)(38,46,50,60)(39,43,51,57)(40,53,47,44)(42,54,56,49)(48,59,62,67)(52,64,61,58)(55,65,66,63);(36,38,47,54,41,50,40,49)(37,42,53,60,45,56,44,46)(39,48,61,65,51,62,52,63)(43,55,64,67,57,66,58,59);(20,22,24,31,25,32,23,30)(21,26,27,29,28,34,33,35)(36,39,41,51)(37,43,45,57)(38,48,50,62)(40,52,47,61)(42,55,56,66)(44,58,53,64)(46,59,60,67)(49,63,54,65);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)(39,51)(43,57)(48,62)(52,61)(55,66)(58,64)(59,67)(63,65)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12656);