Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#13446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| prime radical | C2×C5×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×C8 ◁ G | |
396 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)(12,24)(13,31)(14,21)(15,20)(16,33)(17,36)(18,23)(19,26)(22,34)(25,27)(28,40)(29,32)(30,41)(35,39)(37,38);(10,12,18,30)(11,19,23,40)(13,32,20,38)(14,27,16,35)(15,26,31,28)(17,37,34,29)(21,24,33,41)(22,25,36,39);(7,9)(10,13,14,22,34,21,31,11,18,20,16,36,17,33,15,23)(12,25,26,32,37,40,35,41,30,39,28,38,29,19,27,24)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 6434);