Finite Group Databasebeta

← Group #10696471

Character table — Group #10696471

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222244444444448888888888888888161616161616161616161616242424242424242448484848
order12222222366666664444441212121288881212121224242424242424242244666612121212888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-11-1
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ922222222222222222-2-2-22-2-2-2-2-2000022-2-20000000000000000000000000000020-2
χ1022222222222222222-2-2-22-2-2-2-2-2000022-2-200000000000000000000000000000-202
χ112222222222222222-22-22-2-222220000-2-2-2-200000000002-2000022-2-2000000000000
χ122222222222222222-22-22-2-222220000-2-2-2-20000000000-220000-2-222000000000000
χ132222222222222222-2-22-2-22-2-2-2-20000-2-222000000000000000000000000000020-20
χ142222222222222222-2-22-2-22-2-2-2-20000-2-2220000000000000000000000000000-2020
χ1522222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1622222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1722222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ1822222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ1922222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3002-2−i3−i3i3i3-1-111000000000000
χ2022222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i300-22i3i3−i3−i311-1-1000000000000
χ2122222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-111000000000000
χ2222222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i300-22−i3−i3i3i311-1-1000000000000
χ232-2-22-2-2222-2-2222-2-2222-2-2-222-2-22i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ242-2-22-2-2222-2-2222-2-2222-2-2-222-2-2−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ252-2-22-2-2222-2-2222-2-22-2-22-22-2-22200002-2-2200000000000000000000000022-2-20000
χ262-2-22-2-2222-2-2222-2-22-2-22-22-2-22200002-2-22000000000000000000000000-2-2220000
χ272-2-22-2-2222-2-2222-2-2-22-2-22222-2-20000-22-22000000002-2002-22-20000000000000000
χ282-2-22-2-2222-2-2222-2-2-22-2-22222-2-20000-22-2200000000-2200-22-220000000000000000
χ292-2-22-2-2222-2-2222-2-2-2-2222-2-2-2220000-222-20000000000000000000022-2-200000000
χ302-2-22-2-2222-2-2222-2-2-2-2222-2-2-2220000-222-200000000000000000000-2-22200000000
χ312-2-22-2-222-111-1-1-111222-2-2-2-1-1112i2i−2i−2i-11-11−i−iii−i−iii0000−i3i3i3−i33−33−3000000000000
χ322-2-22-2-222-111-1-1-111222-2-2-2-1-1112i2i−2i−2i-11-11−i−iii−i−iii0000i3−i3−i3i3−33−33000000000000
χ332-2-22-2-222-111-1-1-111222-2-2-2-1-111−2i−2i2i2i-11-11ii−i−iii−i−i0000−i3i3i3−i3−33−33000000000000
χ342-2-22-2-222-111-1-1-111222-2-2-2-1-111−2i−2i2i2i-11-11ii−i−iii−i−i0000i3−i3−i3i33−33−3000000000000
χ352-2-22-2-222-111-1-1-111-22-2-222-1-11100001-11-133−3−3−3−3332-200-11-113−3−33000000000000
χ362-2-22-2-222-111-1-1-111-22-2-222-1-11100001-11-133−3−3−3−333-22001-11-1−333−3000000000000
χ372-2-22-2-222-111-1-1-111-22-2-222-1-11100001-11-1−3−33333−3−32-200-11-11−333−3000000000000
χ382-2-22-2-222-111-1-1-111-22-2-222-1-11100001-11-1−3−33333−3−3-22001-11-13−3−33000000000000
χ3944444444-2-2-2-2-2-2-2-24-4-4-44-422220000-2-22200000000000000000000000000000000
χ4044444444-2-2-2-2-2-2-2-2-4-44-4-442222000022-2-200000000000000000000000000000000
χ41444-4-4-44-44444-4-4-4-400000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ42444-4-4-44-44444-4-4-4-40000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ43444-4-4-44-4-2-2-2-22222000000−2i32i3−2i32i32i−2i2i−2i00002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000
χ44444-4-4-44-4-2-2-2-22222000000−2i32i3−2i32i3−2i2i−2i2i0000−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000
χ45444-4-4-44-4-2-2-2-222220000002i3−2i32i3−2i32i−2i2i−2i00002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000
χ46444-4-4-44-4-2-2-2-222220000002i3−2i32i3−2i3−2i2i−2i2i0000−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000
χ4744-444-4-4-444-4-44-44-4000000000000000000000000000000000000002i−2i2i−2i00000000
χ4844-444-4-4-444-4-44-44-400000000000000000000000000000000000000−2i2i−2i2i00000000
χ4944-4-4-44-4444-4-4-44-440000000000000000000000000000000000000000002-22-20000
χ5044-4-4-44-4444-4-4-44-44000000000000000000000000000000000000000000-22-220000
χ514-444-44-4-44-44-44-4-44000000000000000000000000000000000000002i−2i−2i2i00000000
χ524-444-44-4-44-44-44-4-4400000000000000000000000000000000000000−2i2i2i−2i00000000
χ534-44-44-4-444-44-4-444-40000000000000000000000000000000000000000002-2-220000
χ544-44-44-4-444-44-4-444-4000000000000000000000000000000000000000000-222-20000
χ554-4-44-4-444-222-2-2-2224-4-44-4422-2-20000-222-200000000000000000000000000000000
χ564-4-44-4-444-222-2-2-222-4-4444-422-2-200002-2-2200000000000000000000000000000000
χ574-4-4-4444-44-4-44-4-44400000000002-2-2200002-2-222-2-22000000000000000000000000
χ584-4-4-4444-44-4-44-4-4440000000000-222-20000-222-2-222-2000000000000000000000000
χ594-4-4-4444-4-222-222-2-2000000−2i32i32i3−2i32-2-220000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000
χ604-4-4-4444-4-222-222-2-2000000−2i32i32i3−2i3-222-200001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000
χ614-4-4-4444-4-222-222-2-20000002i3−2i3−2i32i32-2-220000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000000000
χ624-4-4-4444-4-222-222-2-20000002i3−2i3−2i32i3-222-200001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000000000000000
χ6388-888-8-8-8-4-444-44-4400000000000000000000000000000000000000000000000000
χ6488-8-8-88-88-4-4444-44-400000000000000000000000000000000000000000000000000
χ658-888-88-8-8-44-44-444-400000000000000000000000000000000000000000000000000
χ668-88-88-8-88-44-444-4-4400000000000000000000000000000000000000000000000000

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