Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #7555 |
4566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=h,b^a=bd,c^a=ce,i^a=i^2,c^b=cf,i^g=i^4128 conjugacy classes — view the full character table.
| maximal subgroup of | #72242797, AGL(1,𝔽5)×#1438, #72242821, … |
| maximal normal subgroup of | #72242797, AGL(1,𝔽5)×#1438, #72242821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084876);