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×#33844 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
674 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)(24,25,30,34)(26,35,36,54)(27,40,32,52)(28,43,46,42)(29,47,45,33)(31,49,50,38)(37,55,51,44)(39,41,48,53);(24,26,30,36)(25,31,34,50)(27,41,32,53)(28,44,46,55)(29,48,45,39)(33,37,47,51)(35,42,54,43)(38,52,49,40);(21,23)(26,36)(31,50)(35,54)(37,51)(38,49)(39,48)(41,53)(44,55);(24,27,30,32)(25,28,34,46)(26,37,36,51)(29,43,45,42)(31,39,50,48)(33,52,47,40)(35,49,54,38)(41,55,53,44)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26832);