Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#9925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C24×C5 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5)(6,7)(8,9)(10,11)(12,14)(13,15)(16,17)(18,19,23,26)(20,27,29,32)(21,25,22,30)(24,31,33,28);(14,17)(18,20,23,29)(19,24,26,33)(21,28,22,31)(25,32,30,27);(7,9)(10,12)(11,14)(13,16)(15,17)(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 2913);