Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #486 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^166,g^b=g^166,g^c=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323227, #36323228, #36323234, … |
| maximal normal subgroup of | #36323227, #36323228, #36323234, … |
| maximal quotient of | #36324265, #36324820, #36324943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 897);