Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24×C42 |
| direct product | C5×#14274 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C5 | C24 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C24 | C24×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C5 ◁ G | |
1742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5)(7,9)(10,11,12,13)(19,23)(24,26)(25,31)(32,33);(14,15,16,17)(18,19,22,23)(20,26,28,24)(21,25,30,31)(27,33,29,32);(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,20,22,28)(19,24,23,26)(21,29,30,27)(25,33,31,32);(18,21,22,30)(19,25,23,31)(20,27,28,29)(24,32,26,33)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 7262);