Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8610 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#8625 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #380 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | C2×C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,27,25,28,23,33)(22,29,32,34,30,35,31,26)(36,37,39,43,40,42,48,50)(38,44,45,51,46,41,47,49);(20,22,23,31,25,30,24,32)(21,26,27,29,28,34,33,35);(22,30)(26,34)(29,35)(31,32)(36,38,40,46)(37,41,42,44)(39,47,48,45)(43,51,50,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1613);