Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#20571 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C23×C19 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,29)(27,30)(28,31)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(20,21,22,23)(24,26,29,25)(27,30,28,31)(34,40)(37,43)(41,46)(44,47);(24,27,29,28)(25,30,26,31)(32,34,35,41,36,40,42,46)(33,37,38,44,39,43,45,47);(24,28,29,27)(25,30,26,31)1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13559);