Finite Group Databasebeta

← Group #10698433

Character table — Group #10698433

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222234444666224466661212121212124444612121212121212121244881212121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ9222222222-2-2222-2-22-222-2-2-2-2-2-2220000-2200000000000000000000000022-2-20000
χ10222222222-2-2222-2-22-222-2-2-2-2-2-2220000-22000000000000000000000000-2-2220000
χ112222222-2-222222-2-2-2222-2-22222-2-222-2-2-2-22222-2-2-2-2000000000000000000000000
χ122222222-2-222222-2-2-2222-2-22222-2-2-2-222-2-2-2-2-2-22222000000000000000000000000
χ132222222-2-2-2-222222-2-22222-2-2-2-2-2-200002-200000000000000000000000000002-200
χ142222222-2-2-2-222222-2-22222-2-2-2-2-2-200002-20000000000000000000000000000-2200
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-222-1-1-1-2-2-22-1-111-1-1-1-11122-2-211-1-1-1-11111000033−3−333−3−3000000000000
χ20222222-1-2-222-1-1-1-2-2-22-1-111-1-1-1-11122-2-211-1-1-1-111110000−3−333−3−333000000000000
χ21222222-1-2-222-1-1-1-2-2-22-1-111-1-1-1-111-2-222111111-1-1-1-1000033−3−3−3−333000000000000
χ22222222-1-2-222-1-1-1-2-2-22-1-111-1-1-1-111-2-222111111-1-1-1-10000−3−33333−3−3000000000000
χ232222-2-2222222222-2-2-2-2-2-2-222-2-22200002-2000000002i−2i002i−2i2i−2i0000000000000000
χ242222-2-2222222222-2-2-2-2-2-2-222-2-22200002-200000000−2i2i00−2i2i−2i2i0000000000000000
χ252222-2-2222-2-2222-22-22-2-222-2-222220000-2-20000000000000000000000000000002i−2i
χ262222-2-2222-2-2222-22-22-2-222-2-222220000-2-2000000000000000000000000000000−2i2i
χ272222-2-22-2-222222-222-2-2-22222-2-2-2-20000-2200000000002i−2i00002i−2i2i−2i000000000000
χ282222-2-22-2-222222-222-2-2-22222-2-2-2-20000-220000000000−2i2i0000−2i2i−2i2i000000000000
χ292222-2-22-2-2-2-22222-222-2-2-2-2-2-222-2-20000220000000000000000000022-2-200000000
χ302222-2-22-2-2-2-22222-222-2-2-2-2-2-222-2-200002200000000000000000000-2-22200000000
χ312222-2-2-12222-1-1-12-2-2-21111-1-111-1-10000-1133−3−333−3−32i−2i00−ii−ii−i3i3i3−i3000000000000
χ322222-2-2-12222-1-1-12-2-2-21111-1-111-1-10000-1133−3−333−3−3−2i2i00i−ii−ii3−i3−i3i3000000000000
χ332222-2-2-12222-1-1-12-2-2-21111-1-111-1-10000-11−3−333−3−3332i−2i00−ii−iii3−i3−i3i3000000000000
χ342222-2-2-12222-1-1-12-2-2-21111-1-111-1-10000-11−3−333−3−333−2i2i00i−ii−i−i3i3i3−i3000000000000
χ352222-2-2-1-2-222-1-1-1-222-211-1-1-1-1111100001-133−3−3−3−333002i−2ii3−i3−i3i3−ii−ii000000000000
χ362222-2-2-1-2-222-1-1-1-222-211-1-1-1-1111100001-133−3−3−3−33300−2i2i−i3i3i3−i3i−ii−i000000000000
χ372222-2-2-1-2-222-1-1-1-222-211-1-1-1-1111100001-1−3−33333−3−3002i−2i−i3i3i3−i3−ii−ii000000000000
χ382222-2-2-1-2-222-1-1-1-222-211-1-1-1-1111100001-1−3−33333−3−300−2i2ii3−i3−i3i3i−ii−i000000000000
χ39444444-244-4-4-2-2-2-4-44-4-2-2222222-2-200002-200000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-244-4-4-2-2-2-22222220000-2200000000000000000000000000000000
χ414444-4-4-244-4-4-2-2-2-44-4422-2-222-2-2-2-200002200000000000000000000000000000000
χ424444-4-4-2-4-4-4-4-2-2-24-444222222-2-2220000-2-200000000000000000000000000000000
χ4344-4-44-440000-4-4400004-400000000000000000000000000000000002i−2i2i−2i00000000
χ4444-4-44-440000-4-4400004-40000000000000000000000000000000000−2i2i−2i2i00000000
χ4544-4-4-4440000-4-440000-4400000000000000000000000000000000002i−2i−2i2i00000000
χ4644-4-4-4440000-4-440000-440000000000000000000000000000000000−2i2i2i−2i00000000
χ474-44-4004004i−4i4-4-4000000004i−4i00000000000000000000000000000000002-22i−2i0000
χ484-44-4004004i−4i4-4-4000000004i−4i0000000000000000000000000000000000-22−2i2i0000
χ494-44-400400−4i4i4-4-400000000−4i4i00000000000000000000000000000000002-2−2i2i0000
χ504-44-400400−4i4i4-4-400000000−4i4i0000000000000000000000000000000000-222i−2i0000
χ514-4-440044i−4i00-44-40000000000004i−4i2i−2i2-2002i−2i2i−2i2-22-2000000000000000000000000
χ524-4-440044i−4i00-44-40000000000004i−4i−2i2i-2200−2i2i−2i2i-22-22000000000000000000000000
χ534-4-44004−4i4i00-44-4000000000000−4i4i2i−2i-22002i−2i2i−2i-22-22000000000000000000000000
χ544-4-44004−4i4i00-44-4000000000000−4i4i−2i2i2-200−2i2i−2i2i2-22-2000000000000000000000000
χ554-4-4400-24i−4i002-22000000−2i32i30023−23−2i2i2i−2i2-200−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1−31+3−1+31−3000000000000000000000000
χ564-4-4400-24i−4i002-22000000−2i32i30023−23−2i2i−2i2i-2200ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111+3−1−31−3−1+3000000000000000000000000
χ574-4-4400-24i−4i002-220000002i3−2i300−2323−2i2i2i−2i2-200ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1+31−3−1−31+3000000000000000000000000
χ584-4-4400-24i−4i002-220000002i3−2i300−2323−2i2i−2i2i-2200−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111−3−1+31+3−1−3000000000000000000000000
χ594-4-4400-2−4i4i002-22000000−2i32i300−23232i−2i2i−2i-2200ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111−3−1+31+3−1−3000000000000000000000000
χ604-4-4400-2−4i4i002-22000000−2i32i300−23232i−2i−2i2i2-200−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1+31−3−1−31+3000000000000000000000000
χ614-4-4400-2−4i4i002-220000002i3−2i30023−232i−2i2i−2i-2200−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111+3−1−31−3−1+3000000000000000000000000
χ624-4-4400-2−4i4i002-220000002i3−2i30023−232i−2i−2i2i2-200ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1−31+3−1+31−3000000000000000000000000
χ6388-8-88-8-4000044-40000-440000000000000000000000000000000000000000000000
χ6488-8-8-88-4000044-400004-40000000000000000000000000000000000000000000000
χ658-88-800-4008i−8i-44400000000−4i4i000000000000000000000000000000000000000000
χ668-88-800-400−8i8i-444000000004i−4i000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.