Finite Group Databasebeta

← Group #63754

Character table — Group #63754

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size11112222333366668888888888881818181818181818
order1244361212224466121233366612121212121288888888
χ1111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1
χ311-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1ii−i−iii−i−i
χ411-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1−i−iii−i−iii
χ51-1i−i1-1i−i1-1i−i1-1i−i111-1-1-1iii−i−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ61-1i−i1-1i−i1-1i−i1-1i−i111-1-1-1iii−i−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ71-1−ii1-1−ii1-1−ii1-1−ii111-1-1-1−i−i−iiiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ81-1−ii1-1−ii1-1−ii1-1−ii111-1-1-1−i−i−iiii−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ92222222222222222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ102222-1-1-1-12222-1-1-1-12-1-12-1-12-1-12-1-100000000
χ112222-1-1-1-12222-1-1-1-1-12-1-12-1-12-1-12-100000000
χ122222-1-1-1-12222-1-1-1-1-1-12-1-12-1-12-1-1200000000
χ1322-2-222-2-222-2-222-2-2-1-1-1-1-1-111111100000000
χ1422-2-2-1-11122-2-2-1-1112-1-12-1-1-211-21100000000
χ1522-2-2-1-11122-2-2-1-111-12-1-12-11-211-2100000000
χ1622-2-2-1-11122-2-2-1-111-1-12-1-1211-211-200000000
χ172-22i−2i2-22i−2i2-22i−2i2-22i−2i-1-1-1111−i−i−iiii00000000
χ182-22i−2i-11−ii2-22i−2i-11−ii2-1-1-2112i−i−i−2iii00000000
χ192-22i−2i-11−ii2-22i−2i-11−ii-12-11-21−i2i−ii−2ii00000000
χ202-22i−2i-11−ii2-22i−2i-11−ii-1-1211-2−i−i2iii−2i00000000
χ212-2−2i2i2-2−2i2i2-2−2i2i2-2−2i2i-1-1-1111iii−i−i−i00000000
χ222-2−2i2i-11i−i2-2−2i2i-11i−i2-1-1-211−2iii2i−i−i00000000
χ232-2−2i2i-11i−i2-2−2i2i-11i−i-12-11-21i−2ii−i2i−i00000000
χ242-2−2i2i-11i−i2-2−2i2i-11i−i-1-1211-2ii−2i−i−i2i00000000
χ2533333333-1-1-1-1-1-1-1-10000000000001111-1-1-1-1
χ2633333333-1-1-1-1-1-1-1-1000000000000-1-1-1-11111
χ2733-3-333-3-3-1-111-1-111000000000000ii−i−i−i−iii
χ2833-3-333-3-3-1-111-1-111000000000000−i−iiiii−i−i
χ293-33i−3i3-33i−3i-11−ii-11−ii000000000000ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ303-33i−3i3-33i−3i-11−ii-11−ii000000000000−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ313-3−3i3i3-3−3i3i-11i−i-11i−i000000000000ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ323-3−3i3i3-3−3i3i-11i−i-11i−i000000000000−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ336666-3-3-3-3-2-2-2-2111100000000000000000000
χ3466-6-6-3-333-2-22211-1-100000000000000000000
χ356-66i−6i-33−3i3i-22−2i2i1-1i−i00000000000000000000
χ366-6−6i6i-333i−3i-222i−2i1-1−ii00000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.