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×#62831 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
6528 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)(22,23,28,33)(24,34,36,29)(25,32,27,30)(26,31,35,37);(8,14)(12,17)(15,20)(19,21)(22,23)(24,34)(25,30)(26,37)(27,32)(28,33)(29,36)(31,35);(6,7,10,11)(8,12,14,17)(9,13,16,18)(15,19,20,21)(22,24,28,36)(23,29,33,34)(25,35,27,26)(30,37,32,31);(22,25,28,27)(23,30,33,32)(24,35,36,26)(29,37,34,31);(6,8)(7,12)(9,15)(10,14)(11,17)(13,19)(16,20)(18,21)(22,26)(23,31)(24,25)(27,36)(28,35)(29,30)(32,34)(33,37);(6,9)(7,13)(8,15)(10,16)(11,18)(12,19)(14,20)(17,21)(22,27,28,25)(23,32,33,30)(24,26,36,35)(29,31,34,37)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55819);