Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C27 |
| direct product | C5×#36782 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C22×C5×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
1518 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)(8,12)(11,13)(15,18)(19,21)(22,23,27,30)(24,31,25,28)(26,34,35,29)(32,36,33,37);(7,10)(11,13)(22,24,27,25)(23,28,30,31)(26,32,35,33)(29,36,34,37);(6,7)(8,11)(9,10)(12,13)(14,15)(16,19)(17,18)(20,21)(22,25,27,24)(23,28,30,31)(26,33,35,32)(29,36,34,37);(6,7)(8,11)(9,10)(12,13)(14,16,17,20)(15,19,18,21)(22,23)(24,31)(25,28)(26,29)(27,30)(32,37)(33,36)(34,35);(6,8)(7,11)(9,12)(10,13)(22,26)(23,29)(24,32)(25,33)(27,35)(28,36)(30,34)(31,37)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 29770);