Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#34634 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| socle | C23×C5 | C25 |
| prime radical | C25×C5 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C5 ◁ G | |
2374 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)(6,7)(8,9)(10,11,13,15)(12,16,17,14)(18,19)(20,23)(21,25)(22,24)(26,29)(27,30)(28,31)(32,33);(10,12,13,17)(11,14,15,16)(18,20)(19,23)(21,27)(22,26)(24,29)(25,30)(28,32)(31,33);(7,9)(20,26)(23,29)(27,32)(30,33);(19,24)(23,29)(25,31)(30,33);(18,21,22,28)(19,25,24,31)(20,27,26,32)(23,30,29,33)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 27622);