Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C109 ⋊ C4 |
| Sylow | C109 ⋊ #339 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^33,g^e=g^108298 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20295896, #28378708, #28378711, … |
| maximal normal subgroup of | C2×#20295896, #28378708, #28378711, … |
| maximal quotient of | #28377859, #28377863, #28377868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1419);