Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#20401 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C22×C22⋊C4 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×C4×C22⋊C4 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×M16×C19 ◁ G | |
1444 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)(20,21,24,28,25,29,36,42)(22,30,33,44,32,26,37,39)(23,27,35,41,34,40,47,50)(31,43,46,51,45,38,48,49);(20,22)(21,26,29,30)(23,31)(24,33)(25,32)(27,38,40,43)(28,39,42,44)(34,45)(35,46)(36,37)(41,49,50,51)(47,48);(20,23,24,35,25,34,36,47)(21,27,28,41,29,40,42,50)(22,31,33,46,32,45,37,48)(26,38,39,49,30,43,44,51);(23,34)(27,40)(31,45)(35,47)(38,43)(41,50)(46,48)(49,51)1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13389);