Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22⋊C4×C109 ⋊ C4 |
| Sylow | C109 ⋊ #352 |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^33,d^b=de,g^b=g^108,d^c=df,g^d=g^108283 conjugacy classes — view the full character table.
| maximal subgroup of | D109⋊#352, C2×#20295929, #28379284, … |
| maximal normal subgroup of | D109⋊#352, C2×#20295929, #28379284, … |
| maximal quotient of | #28377959, #28377976, #28378013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1452);