Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D109⋊#108 |
| Sylow | C109 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,b^2=d,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^33,g^c=g^108,g^e=g^108460 conjugacy classes — view the full character table.
| maximal subgroup of | #28378091, #28378094, #28378096, … |
| maximal normal subgroup of | #28378091, #28378094, #28378096, … |
| maximal quotient of | D109⋊#334, D109⋊#335, #28378579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1562);