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×#62825 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
6530 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)(7,11)(9,16)(12,17)(15,20)(23,28)(24,32)(25,35)(31,36);(8,14)(12,17)(15,20)(19,21)(22,23,27,28)(24,33,32,29)(25,30,35,37)(26,36,34,31);(6,7,10,11)(8,12,14,17)(9,13,16,18)(15,19,20,21)(22,24,27,32)(23,29,28,33)(25,34,35,26)(30,36,37,31);(22,25)(23,30)(24,34)(26,32)(27,35)(28,37)(29,36)(31,33);(6,8)(7,12)(9,15)(10,14)(11,17)(13,19)(16,20)(18,21)(22,26,27,34)(23,31,28,36)(24,25,32,35)(29,30,33,37);(6,9)(7,13)(8,15)(10,16)(11,18)(12,19)(14,20)(17,21)(22,25)(23,30)(24,34)(26,32)(27,35)(28,37)(29,36)(31,33)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55813);