Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(25,31)(26,30)(27,35)(28,40)(32,48)(33,50)(34,47)(36,43)(37,52)(38,51)(39,45)(41,44)(46,53)(49,54);(24,25,29,34)(26,32,30,44)(27,37,39,50)(28,41,43,48)(31,36,47,40)(33,51,52,38)(35,54,45,46)(42,49,55,53);(21,23)(24,26,29,30)(25,32,34,44)(27,35,39,45)(28,36,43,40)(31,41,47,48)(33,49,52,53)(37,54,50,46)(38,42,51,55);(24,27,29,39)(25,33,34,52)(26,35,30,45)(28,42,43,55)(31,46,47,54)(32,49,44,53)(36,51,40,38)(37,48,50,41)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26825);