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 ⋊ #360 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^33,c^b=cef,d^b=df,e^b=ef,g^b=g^108,g^d=g^108205 conjugacy classes — view the full character table.
| maximal subgroup of | D109⋊#360, C2×#20295943, #28379352, … |
| maximal normal subgroup of | D109⋊#360, C2×#20295943, #28379352, … |
| maximal quotient of | #28377991, #28377992, #28378019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1466);