Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#17964 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C5×C8 | C2×D4 |
| commutator | C2×C4 | C23×C4×C5 |
| Frattini, cosocle | C42 | C24×C5 |
| socle | C22×C5 | C2×C4×D4 |
| prime radical | C5×#3171 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C8 ◁ C2×C4×C5×C8 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5)(6,7)(8,10)(9,11)(12,13)(14,15,19,22,18,21,27,29)(16,23,25,26,24,20,28,17);(7,10)(8,13)(11,12)(14,16)(15,20)(17,22)(18,24)(19,25)(21,23)(26,29)(27,28);(14,17,19,23,18,26,27,20)(15,16,22,25,21,24,29,28);(7,11)(10,12)(15,21)(16,24)(22,29)(25,28)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 10952);