Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | 2−1+4⋊C5 ⋊ C2×C4 |
696 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2,5,2^7|a^2=i,d^2=h,e^2=h,g^2=h,b^a=b^4,c^a=cdef,d^a=df,e^a=efh,c^b=ce,d^b=dfh,e^b=cef,f^b=cd,d^c=dh,e^c=eh,f^c=fh,e^d=eh56 conjugacy classes — view the full character table.
| maximal subgroup of | #72209626, #72209628, #72209630, … |
| maximal normal subgroup of | C2×#13046134 |
| maximal quotient of | C2×#13046134, #72209975 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116402);