Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C5×#62829 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
6636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 37 points:
(1,2,3,4,5)(6,7)(8,14)(9,15)(10,18)(11,12)(13,19)(16,17)(20,21)(23,27)(25,32)(28,33)(31,36);(7,12)(8,15)(13,18)(16,21)(24,30)(28,33)(31,36)(35,37);(6,8)(7,9)(10,16)(11,15)(12,14)(13,17)(18,20)(19,21)(22,23,26,27)(24,28,30,33)(25,29,32,34)(31,35,36,37);(6,9)(7,8)(10,17)(11,14)(12,15)(13,16)(18,21)(19,20);(6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,19)(20,21)(22,24)(23,28)(25,31)(26,30)(27,33)(29,35)(32,36)(34,37);(6,10,11,19)(7,13,12,18)(8,16,15,21)(9,17,14,20)(22,25)(23,29)(24,31)(26,32)(27,34)(28,35)(30,36)(33,37)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55817);