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×#36716 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C2×C5×#538 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
2406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5)(6,7,8,9)(12,16)(15,17)(18,19)(20,27)(21,22)(23,31)(24,26)(25,32)(28,30)(29,33);(11,14)(15,17)(18,20,24,21)(19,22,26,27)(23,28,32,29)(25,30,31,33);(6,7)(8,9)(10,11)(12,15)(13,14)(16,17)(18,21,24,20)(19,22,26,27)(23,29,32,28)(25,30,31,33);(10,11)(12,15)(13,14)(16,17)(18,22)(19,20)(21,26)(23,30)(24,27)(25,28)(29,31)(32,33);(10,12)(11,15)(13,16)(14,17)(18,23)(19,25)(20,28)(21,29)(22,30)(24,32)(26,31)(27,33)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 29704);