Table 1 Isotropy subgroups of D8 × T.
SubgroupSubspace dimensionGeneratorsPhase pattern
D81σ, κ{a, a, a, a, a, a, a, a}
D8(+, –)1(κ, 1), (κσ, –1){a, –a, a, –a, a, –a, a, –a}
Z8(p), p ∈ 1, 2, 31σωp{a, ωpa, ω2pa, ω3pa, ω4pa,
ω5pa, ω6pa, ω7pa}
D4(+, –)1(σκ, 1), (κσ, –1){a, a, –a, –a, a, a, –a, –a}
D4(κ)2σ2κ, κ{a, b, a, b, a, b, a, b}
Z4(p), p ∈ 1, 22σ2ω2p{a, b, ipa, ipb, i2pa, i2pb, i3pa, i3pb}
D2(κ)3σ4κ, κ{a, b, c, b, a, b, c, b}
D1(κ)5κ{a, b, c, d, e, d, c, b}
D2(κσ)2σ3κ, κσ{a, b, b, a, a, b, b, a}
D1(κσ)4σ7κ, κσ{a, b, c, d, d, c, b, a}
D2(–, –)23κ, –1), (κσ, –1){a, b, –b, –a, a, b, –b, –a}
D1(–, –)47κ, –1), (κσ, –1){a, b, c, d, –d, –c, –b, –a}
D2(+, –)23κ, 1), (κσ, –1){a, b, b, a, –a, –b, –b, –a}
Z24σ4{a, b, c, d, a, b, c, d}
Z2(p = 1)4σ4ω4{a, b, c, d, –a, –b, –c, –d}