Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C2×C5×H(5,𝔽2) ⋊ C4 |
| Sylow | C5 ⋊ #62652 |
11674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=h,b^a=bg,f^a=fg,i^a=i^2,e^b=eg,d^c=dg,i^h=i^4164 conjugacy classes — view the full character table.
| maximal subgroup of | #72221967, #72253755, AGL(1,𝔽5)×H(7,𝔽2), … |
| maximal normal subgroup of | #72221967, #72253755, AGL(1,𝔽5)×H(7,𝔽2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116287);