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×#36769 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C5×#2688 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
1566 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)(18,21)(22,23)(24,25)(26,30)(27,28)(29,33)(31,32)(34,35)(36,37);(7,10)(11,13)(14,15,17,19)(16,18,20,21)(23,28)(24,29)(30,35)(31,36);(6,7)(8,11)(9,10)(12,13)(14,16,17,20)(15,18,19,21)(22,24,27,29)(23,25,28,33)(26,31,34,36)(30,32,35,37);(6,7)(8,11)(9,10)(12,13)(22,25)(23,29)(24,28)(26,32)(27,33)(30,36)(31,35)(34,37);(6,8)(7,11)(9,12)(10,13)(22,26,27,34)(23,30,28,35)(24,31,29,36)(25,32,33,37)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 29757);