Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#23603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C24×C5 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5)(10,11,16,19,15,20,14,28)(12,21,30,32,23,38,24,17)(13,18,29,34,27,35,26,36)(22,37,40,31,39,33,25,41);(6,7)(8,9)(10,12,14,24,15,23,16,30)(11,17,19,21,20,32,28,38)(13,25,26,39,27,40,29,22)(18,33,34,41,35,37,36,31);(7,9)(10,13,15,27)(11,18,20,35)(12,22,23,39)(14,29,16,26)(17,31,32,41)(19,36,28,34)(21,37,38,33)(24,40,30,25);(12,23)(17,32)(21,38)(22,39)(24,30)(25,40)(31,41)(33,37)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 16591);