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×#35326 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C2×C5×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
2182 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)(11,14)(15,17)(18,19,23,27)(20,21,25,24)(22,30,31,26)(28,32,33,29);(6,7,8,9)(20,25)(21,24)(28,33)(29,32);(10,11,13,14)(12,15,16,17)(18,20,23,25)(19,24,27,21)(22,28,31,33)(26,32,30,29);(10,12,13,16)(11,15,14,17)(18,21,23,24)(19,25,27,20)(22,29,31,32)(26,33,30,28);(18,22,23,31)(19,26,27,30)(20,28,25,33)(21,29,24,32)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28314);