Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D8×C109 ⋊ C4 |
| Sylow | C109 ⋊ #357 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^33,c^b=ce,e^b=ef,g^d=g^108211 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20295938, #28379339, #28379340, … |
| maximal normal subgroup of | C2×#20295938, #28379339, #28379340, … |
| maximal quotient of | #28377986, #28377987, #28378018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1461);