Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C109 ⋊ C4 |
| Sylow | C109 ⋊ #354 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^33,c^b=cf,d^b=def,d^c=df,g^d=g^108283 conjugacy classes — view the full character table.
| maximal subgroup of | #28378155, #28378156, C2×#20295932, … |
| maximal normal subgroup of | #28378155, #28378156, C2×#20295932, … |
| maximal quotient of | #28377962, #28377973, #28378012, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1455);