Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×Q8×C109 ⋊ C4 |
| Sylow | C109 ⋊ #410 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,c^2=f,b^a=bd,d^a=df,g^a=g^33,e^b=ef,g^b=g^108,g^c=g^108,g^e=g^108292 conjugacy classes — view the full character table.
| maximal subgroup of | #28378134, #28378791, #28378881, … |
| maximal normal subgroup of | #28378134, #28378791, #28378881, … |
| maximal quotient of | #28378266, #28378273, #28378275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1530);