Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
990 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)(20,21,26,30,27,31,25,41)(22,32,34,28,35,45,42,46)(23,36,38,47,24,39,40,29)(33,44,50,51,37,43,49,48);(20,22,26,34,27,35,25,42)(21,28,30,45,31,46,41,32)(23,37,38,49,24,33,40,50)(29,44,36,51,47,43,39,48);(20,23,27,24)(21,29,31,47)(22,33,35,37)(25,38,26,40)(28,43,46,44)(30,39,41,36)(32,48,45,51)(34,49,42,50);(20,24,27,23)(21,29,31,47)(22,33,35,37)(25,38,26,40)(28,44,46,43)(30,36,41,39)(32,48,45,51)(34,50,42,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18187);