Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#10538 |
| 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 | |
486 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)(12,14)(13,16)(15,17)(18,19,23,27)(20,25,29,33)(21,30,28,24)(22,32,31,26);(10,11)(12,14)(13,16)(15,17)(18,20,23,29)(19,24,27,30)(21,31,28,22)(25,26,33,32);(7,9)(11,14)(12,17)(15,16)(18,21,22,20,23,28,31,29)(19,25,26,30,27,33,32,24)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 3526);