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×#62828 |
| 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)(8,10)(9,17)(11,12)(13,15)(14,19)(16,20)(18,21)(23,27)(25,32)(28,33)(31,36);(7,12)(8,15)(14,17)(16,21)(24,30)(28,33)(31,36)(35,37);(6,8,11,15)(7,13,12,10)(9,16,19,21)(14,20,17,18)(22,23,26,27)(24,28,30,33)(25,29,32,34)(31,35,36,37);(6,9)(7,14)(8,16)(10,18)(11,19)(12,17)(13,20)(15,21);(6,7)(8,13)(9,14)(10,15)(11,12)(16,20)(17,19)(18,21)(22,24)(23,28)(25,31)(26,30)(27,33)(29,35)(32,36)(34,37);(6,10,11,13)(7,15,12,8)(9,18,19,20)(14,21,17,16)(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, 55816);