Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C5×#62817 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
9494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 6 generators on 21 points:
(1,2,3,4,5)(6,7)(8,14)(9,13)(10,12)(11,15)(16,18)(17,20)(19,21);(6,8)(7,11)(9,15)(10,16)(12,19)(13,14)(17,21)(18,20);(7,12)(8,15)(11,18)(13,20)(14,19)(16,21);(7,13)(11,14)(12,20)(18,19);(8,16)(11,19)(14,18)(15,21);(7,12)(11,19)(13,20)(14,18)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55805);