Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D167)⋊C16 |
| Fitting | C2×C16×C167 ⋊ C2 |
| 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^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C16×D167, C2×(C2×D167)⋊C16, #36325747, … |
| maximal normal subgroup of | C22⋊C16×D167, C2×(C2×D167)⋊C16, #36325747, … |
| maximal quotient of | #36322061, #36322077, #36322092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 328);