Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
566 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)(22,30)(23,33)(24,36)(26,39)(28,43)(29,42)(31,47)(32,35)(34,49)(37,50)(38,48)(40,46)(41,44)(45,51);(20,21)(22,26)(23,34)(24,29)(25,27)(28,37)(30,46)(31,40)(32,41)(33,49)(35,51)(36,42)(38,45)(39,47)(43,50)(44,48);(20,22,24,38,25,31,36,32)(21,26,29,45,27,40,42,41)(23,35,33,47,37,48,50,30)(28,44,43,46,34,51,49,39);(21,27)(26,40)(28,34)(29,42)(39,46)(41,45)(43,49)(44,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26645);