Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#22694 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | D42 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | D4×C4⋊C4 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ G | |
812 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)(20,21,26,31,27,32,25,44)(22,33,35,28,37,46,36,47)(23,38,34,48,40,45,39,29)(24,30,41,50,43,51,42,49);(20,22)(21,28)(23,24)(25,36)(26,35)(27,37)(29,30)(31,46)(32,47)(33,44)(34,41)(38,50)(39,42)(40,43)(45,49)(48,51);(20,23,25,39,27,40,26,34)(21,29,31,38,32,48,44,45)(22,24,36,42,37,43,35,41)(28,30,46,50,47,51,33,49);(20,24)(21,30)(22,34)(23,36)(25,42)(26,41)(27,43)(28,45)(29,46)(31,50)(32,51)(33,48)(35,40)(37,39)(38,47)(44,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15682);