Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9109 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#10974 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #386 |
| commutator | C24 | C22×C4×C5 |
| Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C22×C5×#41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
1258 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)(10,11,14,19,15,18,27,33)(12,20,22,34,23,16,26,29)(13,17,25,32,24,31,37,41)(21,30,36,40,35,28,38,39);(10,12,15,23)(11,16,18,20)(13,21,24,35)(14,26,27,22)(17,30,31,28)(19,34,33,29)(25,38,37,36)(32,39,41,40);(7,9)(10,13)(11,17)(12,21)(14,25)(15,24)(16,28)(18,31)(19,32)(20,30)(22,36)(23,35)(26,38)(27,37)(29,39)(33,41)(34,40)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 3962);