Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#35319 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C24×C5 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
2026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5)(7,9)(10,11,13,15)(12,14,16,17)(19,24)(22,30)(25,26)(28,29);(10,11)(12,14)(13,15)(16,17)(18,19)(20,26)(21,25)(22,27)(23,24)(28,33)(29,32)(30,31);(6,7,8,9)(10,11)(12,14)(13,15)(16,17)(18,20,23,21)(19,25,24,26)(22,28,30,29)(27,32,31,33);(10,12,13,16)(11,14,15,17)(18,21,23,20)(19,26,24,25)(22,29,30,28)(27,33,31,32);(18,22,23,30)(19,27,24,31)(20,28,21,29)(25,32,26,33)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28307);