Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C27 |
| direct product | C5×#35323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C24×C5 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
1558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5)(7,10)(11,13)(15,19)(16,21)(22,23,27,24)(25,28,32,30)(26,31,34,29)(33,36,37,35);(14,15)(16,20)(17,21)(18,19)(23,24)(25,32)(29,31)(33,37);(6,7)(8,11)(9,10)(12,13)(14,16,18,21)(15,20,19,17)(22,24,27,23)(25,30,32,28)(26,31,34,29)(33,36,37,35);(6,8,9,12)(7,11,10,13)(14,17,18,20)(15,21,19,16)(22,25)(23,28)(24,30)(26,33)(27,32)(29,35)(31,36)(34,37);(22,26,27,34)(23,29,24,31)(25,33,32,37)(28,35,30,36)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28311);