Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1262 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)(22,32,36,27)(23,29,24,38)(25,31)(26,30)(28,37,46,39)(33,49)(34,43)(35,48,40,44)(41,47)(42,50)(45,51);(20,22)(21,27)(23,33)(24,34)(25,40)(26,36)(28,45)(29,43)(30,32)(31,48)(35,41)(37,51)(38,49)(39,50)(42,46)(44,47);(20,23,26,24)(21,28,30,46)(22,33,36,34)(25,39,41,37)(27,42,32,45)(29,31,38,47)(35,51,40,50)(43,44,49,48);(20,24,26,23)(21,29,30,38)(22,34,36,33)(25,39,41,37)(27,43,32,49)(28,31,46,47)(35,51,40,50)(42,44,45,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14773);