Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C109 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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=e,d^2=f,b^a=bd,d^a=df,g^a=g^108,d^b=df,g^b=g^108,g^c=g^108784 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SD16×D109, C2×#20295117, C4×#16812718, … |
| maximal normal subgroup of | C4×SD16×D109, C2×#20295117, C4×#16812718, … |
| maximal quotient of | #28361835, #28361865, #28361878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 640);