Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C167 ⋊ C2 |
| Sylow | C167 ⋊ #350 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^166,c^b=cf,d^b=df,g^b=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D167, C2×#24923054, #36325764, … |
| maximal normal subgroup of | #350×D167, C2×#24923054, #36325764, … |
| maximal quotient of | #36322063, #36322079, #36322092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 334);