Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×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,g^b=g^108,d^c=df,g^d=g^108445 conjugacy classes — view the full character table.
| maximal subgroup of | #28378159, #28378160, #28378161, … |
| maximal normal subgroup of | #28378159, #28378160, #28378161, … |
| maximal quotient of | #28377963, #28377972, #28378013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1456);