Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C167 ⋊ C2 |
| Sylow | C167 ⋊ #357 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=ce,e^b=ef,g^b=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #357×D167, C2×#24923069, #36325843, … |
| maximal normal subgroup of | #357×D167, C2×#24923069, #36325843, … |
| maximal quotient of | #36322098, #36322146, #36322183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 349);