Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D109⋊(C22⋊C8) |
| Sylow | C109 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 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,e^2=f,b^a=bd,g^a=g^33,g^c=g^108,g^e=g^108472 conjugacy classes — view the full character table.
| maximal subgroup of | #28377869, #28377874, #28377894, … |
| maximal normal subgroup of | #28377869, #28377874, #28377894, … |
| maximal quotient of | D109⋊#323, D109⋊#324, #28378264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1517);