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×#20532 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
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)(26,30)(27,29)(28,31)(32,33,35,39,36,38,42,45)(34,37,41,44,40,43,46,47);(20,21,22,23)(24,26)(25,28)(27,31)(29,30)(34,40)(37,43)(41,46)(44,47);(26,31)(28,30)(32,34)(33,37)(35,41)(36,40)(38,43)(39,44)(42,46)(45,47);(25,29)(28,30)(33,38)(34,40)(39,45)(41,46)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13520);