Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D109⋊#100 |
| Sylow | C109 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,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 | #28378115, #100×#89137, #28378878, … |
| maximal normal subgroup of | #28378115, #100×#89137, #28378878, … |
| maximal quotient of | D109⋊#323, #28378272, #28378273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1532);