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×#35325 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C25×C5 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
2370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5)(7,9)(11,14)(15,17)(18,19,23,21)(20,26,27,24)(22,29,30,25)(28,31,33,32);(6,7)(8,9)(19,21)(20,27)(25,29)(28,33);(10,11,13,14)(12,15,16,17)(18,20,23,27)(19,24,21,26)(22,28,30,33)(25,31,29,32);(10,12,13,16)(11,15,14,17)(18,21,23,19)(20,26,27,24)(22,29,30,25)(28,32,33,31);(18,22,23,30)(19,25,21,29)(20,28,27,33)(24,31,26,32)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28313);