Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D109⋊#101 |
| Sylow | C109 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,b^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^33,e^b=ef,g^c=g^108,g^e=g^108292 conjugacy classes — view the full character table.
| maximal subgroup of | #28378128, #101×#89137, #28378879, … |
| maximal normal subgroup of | #28378128, #101×#89137, #28378879, … |
| maximal quotient of | D109⋊#324, #28378275, #28378276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1534);