Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#10541 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C5 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C5 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5)(6,7)(8,9)(10,11,15,17)(12,13,16,14)(19,23)(20,26)(21,29)(24,32)(25,30)(27,31);(10,12)(11,13)(14,17)(15,16)(18,19,22,25)(20,27,26,24)(21,30,29,23)(28,31,33,32);(7,9)(11,16)(12,17)(13,14)(18,20,21,28,22,26,29,33)(19,24,23,31,25,27,30,32)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 3529);