Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,32,37)(30,39,43,54)(31,36,34,46)(33,49,48,56)(35,50,40,44)(38,47,52,41)(42,53,45,59)(51,57,55,58);(21,24)(25,27)(28,29)(30,40)(31,46)(32,37)(33,38)(34,36)(35,43)(39,50)(41,49)(42,51)(44,54)(45,55)(47,56)(48,52)(53,58)(57,59);(28,30,41,57,34,45,48,50,32,43,47,58,31,42,33,44)(29,35,49,53,36,51,52,54,37,40,56,59,46,55,38,39);(20,22,23,26)(21,25,24,27)(28,31,32,34)(29,36,37,46)(30,42,43,45)(33,47,48,41)(35,51,40,55)(38,49,52,56)(39,53,54,59)(44,58,50,57)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26733);