Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C109 ⋊ C2 |
| Sylow | C109 ⋊ #497 |
124 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^b=g^108772 conjugacy classes — view the full character table.
| maximal subgroup of | #28362337, #28362342, #28362347, … |
| maximal normal subgroup of | #28362337, #28362342, #28362347, … |
| maximal quotient of | #28362657, #28362664, #28362676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 941);