Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#446 ⋊ C4 |
| Sylow | C5 ⋊ #20518 |
838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=eg,d^2=ef,f^2=h,b^a=be,d^a=dh,c^b=ch,i^b=i^3,i^c=i^2,i^g=i^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #72269233, #72269248 |
| maximal normal subgroup of | #72269233, #72269248 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104108);