Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C109 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^33,c^b=ce,g^b=g^108,g^d=g^108298 conjugacy classes — view the full character table.
| maximal subgroup of | D109⋊(D4⋊C8), C2×#20295874, #28378325, … |
| maximal normal subgroup of | D109⋊(D4⋊C8), C2×#20295874, #28378325, … |
| maximal quotient of | #28377849, #28377851, #28377868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1397);