Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33887 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3339 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
548 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)(20,21,23,25)(22,26,27,24)(28,29,34,38)(30,35,33,49)(31,41,44,58)(32,45,48,57)(36,51,53,43)(37,40,55,47)(39,56,42,54)(46,50,59,52);(20,22)(21,24)(23,27)(25,26)(28,30,34,33)(29,35,38,49)(31,42,44,39)(32,40,48,47)(36,52,53,50)(37,45,55,57)(41,54,58,56)(43,59,51,46);(28,31,34,44)(29,36,38,53)(30,39,33,42)(32,46,48,59)(35,50,49,52)(37,54,55,56)(40,51,47,43)(41,57,58,45);(22,27)(24,26)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26875);