Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic167⋊C16 |
| Sylow | C167 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C16×D167, C2×Dic167⋊C16, #36325892, … |
| maximal normal subgroup of | C4⋊C16×D167, C2×Dic167⋊C16, #36325892, … |
| maximal quotient of | #36322201, #36322207, #36322215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 367);