Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#13479 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| prime radical | C23×C5 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×C8 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5)(6,7,8,9)(10,11)(12,15)(13,23)(14,19)(16,24)(17,22)(18,27)(20,32)(21,30)(25,34)(26,37)(28,35)(29,39)(31,38)(33,36)(40,41);(10,12,15,11,16,19,31,21,17,20,32,22,30,38,14,24)(13,25,27,39,28,40,41,35,29,18,34,23,33,37,26,36);(7,9)(10,13,17,29)(11,18,22,25)(12,23,20,39)(14,27,31,34)(15,26,32,41)(16,33,30,28)(19,35,38,36)(21,40,24,37)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 6467);