Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#10375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C24×C5 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5)(7,10)(8,12)(11,13)(14,15)(16,22,24,28)(17,20)(18,21)(19,25,23,26)(27,29);(14,15)(16,23,24,19)(17,20)(18,21)(22,25,28,26)(27,29);(6,7,9,11)(8,13,12,10)(14,16)(15,19)(17,26)(18,24)(20,28)(21,23)(22,29)(25,27)185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 3363);