Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C109 ⋊ C4 |
| Sylow | C109 ⋊ #344 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^76,d^b=df,g^b=g^33,g^d=g^108,g^e=g^108292 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20295909, #28378744, #28378789, … |
| maximal normal subgroup of | C2×#20295909, #28378744, #28378789, … |
| maximal quotient of | #28377871, #28377873, #28377878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1432);