Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11724786 |
| Sylow | C109 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^33,c^b=ce,g^d=g^108298 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#11724786, D109⋊(Q8⋊C8), #28378323, … |
| maximal normal subgroup of | C2×Q8⋊#11724786, D109⋊(Q8⋊C8), #28378323, … |
| maximal quotient of | #28377850, #28377852, #28377868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1398);