Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C167 ⋊ C2 |
| Sylow | C167 ⋊ #360 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^166,c^b=cef,d^b=df,e^b=ef,g^b=g^1661676 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #360×D167, C2×#24923080, #36325872, … |
| maximal normal subgroup of | #360×D167, C2×#24923080, #36325872, … |
| maximal quotient of | #36322106, #36322109, #36322148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 360);