Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #7333 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,g^2=h,b^a=be,d^a=dgh,f^a=fh,c^b=cgh,e^b=eh,i^b=i^4,d^c=dh134 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#7333, #72242226, #72242232, … |
| maximal normal subgroup of | D5×#7333, #72242226, #72242232 |
| maximal quotient of | #72242280, #72269182 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 56903);