Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#23751 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#400 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
664 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)(20,21,24,28,25,29,31,40)(22,30,33,42,34,45,39,26)(23,35,38,49,37,27,43,44)(32,46,47,48,36,50,51,41);(20,22,31,33,25,34,24,39)(21,26,40,30,29,42,28,45)(23,36,43,51,37,32,38,47)(27,41,49,46,35,48,44,50);(20,23,24,38,25,37,31,43)(21,27,28,44,29,35,40,49)(22,32,33,47,34,36,39,51)(26,41,30,46,42,48,45,50);(23,37)(27,35)(32,36)(38,43)(41,48)(44,49)(46,50)(47,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16739);