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×#36705 |
| 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)(7,9)(12,16)(15,17)(19,20)(21,28)(22,30)(31,32);(11,14)(15,17)(18,19,23,20)(21,26,28,24)(22,25,30,27)(29,32,33,31);(6,7)(8,9)(10,11)(12,15)(13,14)(16,17)(18,20,23,19)(21,26,28,24)(22,27,30,25)(29,32,33,31);(10,11)(12,15)(13,14)(16,17)(18,21)(19,24)(20,26)(22,29)(23,28)(25,31)(27,32)(30,33);(10,12)(11,15)(13,16)(14,17)(18,22)(19,25)(20,27)(21,29)(23,30)(24,31)(26,32)(28,33)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 29693);