Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C29 |
| direct product | C2×C5×#1439 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C5 | C23 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C24 | C24×C5 |
| prime radical | C26×C5 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C5 ◁ G | |
4926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(19,20,21,22,23);(8,10)(11,12,13,14)(16,18);(4,6)(8,10)(15,16,17,18);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 6824);