Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q16×C109 ⋊ C4 |
| Sylow | C109 ⋊ #358 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=f,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×#20295939, #28379339, #28379340, … |
| maximal normal subgroup of | C2×#20295939, #28379339, #28379340, … |
| maximal quotient of | #28377988, #28377989, #28378020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1462);