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×#36804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C5×#392 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
1534 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)(16,20)(19,21)(22,23,27,28)(24,29,31,26)(25,33,35,30)(32,34,37,36);(7,10)(11,13)(14,15,18,17)(16,19,20,21)(23,28)(24,31)(30,33)(32,37);(6,7)(8,11)(9,10)(12,13)(14,16)(15,19)(17,21)(18,20)(22,24)(23,29)(25,32)(26,28)(27,31)(30,36)(33,34)(35,37);(6,7)(8,11)(9,10)(12,13)(14,17,18,15)(16,21,20,19)(22,25,27,35)(23,30,28,33)(24,32,31,37)(26,34,29,36);(6,8)(7,11)(9,12)(10,13)(22,26,27,29)(23,24,28,31)(25,34,35,36)(30,32,33,37)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 29792);