Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25,27,29)(26,30,31,28)(33,37)(34,40)(35,43)(45,47);(24,25,27,29)(26,28,31,30)(32,33,36,37)(34,41,40,38)(35,39,43,44)(42,47,46,45);(24,25)(26,28)(27,29)(30,31)(32,33)(34,38)(35,39)(36,37)(40,41)(42,45)(43,44)(46,47);(20,22,23,21)(24,26,27,31)(25,28,29,30)(32,34,36,40)(33,38,37,41)(35,42,43,46)(39,45,44,47);(32,35,36,43)(33,39,37,44)(34,42,40,46)(38,45,41,47)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27463);