Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33595 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
706 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(22,30)(23,34)(24,35)(27,41)(28,39)(29,45)(31,36)(32,47)(33,48)(37,49)(38,43)(42,46)(44,51);(20,21,23,26,25,28,34,39)(22,27,31,38,33,42,32,44)(24,29,35,40,37,45,49,50)(30,43,47,41,48,51,36,46);(20,22)(21,27)(23,31)(24,36)(25,33)(26,38)(28,42)(29,46)(30,35)(32,34)(37,47)(39,44)(40,43)(41,45)(48,49)(50,51);(21,28)(26,39)(27,42)(29,45)(38,44)(40,50)(41,46)(43,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26583);