Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #423 |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,b^2=d,e^2=f,b^a=bd,c^a=cf,g^c=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322561, #36322565, #36322574, … |
| maximal normal subgroup of | #36322561, #36322565, #36322574, … |
| maximal quotient of | #36322892, #36322895, #36322898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 571);