Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#32950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1282 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)(24,37)(28,39)(29,40)(31,47)(32,33)(34,35)(38,42)(41,50)(44,45)(46,48);(20,21,24,26,25,29,37,40)(22,27,32,38,33,43,30,42)(23,28,34,39,36,45,35,44)(31,41,47,49,48,50,46,51);(20,22)(21,27)(23,31)(24,32)(25,33)(26,38)(28,41)(29,43)(30,37)(34,47)(35,46)(36,48)(39,49)(40,42)(44,51)(45,50);(20,23)(21,28)(22,31)(24,34)(25,36)(26,39)(27,41)(29,45)(30,46)(32,47)(33,48)(35,37)(38,49)(40,44)(42,51)(43,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25938);