Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C109 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^108,d^b=de,d^c=df769 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D109, C2×#20294813, #28364670, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D109, C2×#20294813, #28364670, … |
| maximal quotient of | #28360960, #28360980, #28361029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 336);