Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C5×H(5,𝔽2) ⋊ C4 |
| Sylow | C5 ⋊ #20616 |
3986 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^2,e^b=eh,f^b=fh,e^c=eh,i^g=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3019, #72221412, #72221462, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3019, #72221412, #72221462, … |
| maximal quotient of | #72226461 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104468);