Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D109⋊#104 |
| Fitting | #41×C109 ⋊ C4 |
| Sylow | C109 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,109|a^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^33,d^b=df,g^c=g^108,g^e=g^108298 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#89137, #28378797, #28378806, … |
| maximal normal subgroup of | #104×#89137, #28378797, #28378806, … |
| maximal quotient of | D109⋊(D4⋊C8), D109⋊(Q8⋊C8), #28378323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1544);