Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#21718 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C5 | C24 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C22×C4 | C24×C5 |
| socle, prime radical | C23×C5 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C5 ◁ G | |
774 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5)(7,9)(10,11)(12,17)(13,15)(14,16)(18,19,24,26,23,27,21,22)(20,28,29,30,31,25,32,33);(10,12,14,13)(11,15,16,17)(18,20,23,31)(19,25,27,28)(21,32,24,29)(22,30,26,33);(6,7,8,9)(18,21,23,24)(19,26,27,22)(20,29,31,32)(25,30,28,33);(10,13,14,12)(11,15,16,17)(18,22,21,27,23,26,24,19)(20,30,32,28,31,33,29,25)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 14706);