Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C27×C4 |
| direct product | C19×#34187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2250 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)(20,21,22,23)(26,30)(28,31)(32,33,37,35)(34,40,42,38)(36,43,44,39)(41,45,47,46);(24,25,27,29)(26,28,30,31)(33,35)(38,40)(39,43)(45,46);(24,26,27,30)(25,28,29,31)(32,34,37,42)(33,38,35,40)(36,41,44,47)(39,45,43,46);(32,35,37,33)(34,40,42,38)(36,43,44,39)(41,46,47,45);(32,36)(33,39)(34,41)(35,43)(37,44)(38,45)(40,46)(42,47)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27175);