Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×C8×D4 ⋊ C4 |
| Sylow | C5 ⋊ #20484 |
1194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=g,d^2=f,f^2=h,b^a=be,c^a=ch,i^b=i^3,i^c=i^2,i^g=i^4152 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, 1103988);