Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C5×#7982 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | #95 |
| commutator | C2×C4 | C2×C42×C5 |
| Frattini, cosocle | C23×C4 | C23×C5 |
| socle | C22×C5 | C2×#95 |
| prime radical | C25×C5 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C24×C4×C5 ◁ G | |
986 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)(6,7)(8,12,13,10)(9,11)(14,15)(16,24)(17,21)(18,22)(19,23)(20,25)(26,29)(27,28);(6,8)(7,10)(9,13)(11,12)(14,16,18,26,19,27,17,25)(15,20,21,28,23,29,22,24);(14,17,19,18)(15,21,23,22)(16,25,27,26)(20,28,29,24)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 970);