Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #7457 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,d^b=dgh,f^b=fh,i^b=i^4,d^c=dh98 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#7457, #72242236, #72242240 |
| maximal normal subgroup of | D5×#7457, #72242236, #72242240 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 57237);