Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #431 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^166,g^c=g^1661700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322517, #36322519, #36322527, … |
| maximal normal subgroup of | #36322517, #36322519, #36322527, … |
| maximal quotient of | #36323882, #36323895, C4⋊C8×Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 601);