Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(C167⋊C16) |
| Sylow | C167 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322061, #36322062, #36322063, … |
| maximal normal subgroup of | #36322061, #36322062, #36322063, … |
| maximal quotient of | #36322062, #36322078, D4⋊(C167⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 329);