Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#36742 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C2×C5×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
2038 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5)(7,9)(12,16)(15,17)(18,19,23,27)(20,25,21,24)(22,30,31,26)(28,32,29,33);(11,14)(15,17)(18,20,23,21)(19,24,27,25)(22,29,31,28)(26,33,30,32);(6,7,8,9)(10,11)(12,15)(13,14)(16,17)(18,21,23,20)(19,25,27,24)(22,29,31,28)(26,33,30,32);(10,11)(12,15)(13,14)(16,17)(18,22,23,31)(19,26,27,30)(20,28,21,29)(24,32,25,33);(10,12)(11,15)(13,16)(14,17)(18,19)(20,24)(21,25)(22,26)(23,27)(28,32)(29,33)(30,31)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 29730);