Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD32×C109 ⋊ C2 |
| Sylow | C109 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^108,g^c=g^108616 conjugacy classes — view the full character table.
| maximal subgroup of | #508×D109, C2×#20295457, #28376164, … |
| maximal normal subgroup of | #508×D109, C2×#20295457, #28376164, … |
| maximal quotient of | #28364736, #28364738, #28364815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 980);