Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #103×C109 ⋊ C2 |
| Sylow | C109 ⋊ #419 |
150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 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,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,c^b=cf,d^b=df,g^c=g^108778 conjugacy classes — view the full character table.
| maximal subgroup of | #419×D109, C2×#20295033, #28371547, … |
| maximal normal subgroup of | #419×D109, C2×#20295033, #28371547, … |
| maximal quotient of | #28361425, #28361451, #28361477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 556);