Finite Group Databasebeta

← Group #69942

Character table — Group #69942

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444422223444466666661212121212121212246666888888881212121224242424242424242424242424242424444444442444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1-1-11
χ611111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-111-1
χ711111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-111-1
χ811111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1-1-11
χ91111-1-1-1-111-1-1111-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1111-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1111-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ121111-1-1-1-111-1-1111-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ131111-1-1-1-1-1-1111-1-11111-1-1-1-11-1-1-1-11111-11-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-1
χ141111-1-1-1-1-1-1111-1-11111-1-1-1-11-1-1-1-11111-11-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-11
χ151111-1-1-1-1-1-1111-1-11111-1-1-1-11-1-1-1-11111-11-1-111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11-11
χ161111-1-1-1-1-1-1111-1-11111-1-1-1-11-1-1-1-11111-11-1-111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-11-1
χ17222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ18222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ192222222222-2-22-2-222222222222222222-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ202222222222-2-2-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ212222222222-2-2-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ2222222222-2-222222-2-222-2-2-2-222222-2-2-2-2-2-2-2-22200000000-2-2220000000000000000000000000000
χ2322222222-2-222-122-2-2-1-11111-1-1-1-1-11111-2-211-1-10000000011-1-133−3−333−3−3−3−333−3−333000000000000
χ2422222222-2-222-122-2-2-1-11111-1-1-1-1-11111-2-211-1-10000000011-1-1−3−333−3−33333−3−333−3−3000000000000
χ2522222222-2-2-2-2-1-2-2-2-2-1-11111-1-1-1-1-1111122-1-1112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ2622222222-2-2-2-2-1-2-2-2-2-1-11111-1-1-1-1-1111122-1-111−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i000000000000
χ272222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-22-2222200000000-2-2-2-20000000000000000000000000000
χ282222-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-1-1-100000000111133−3−3−3−33333−3−3−3−333000000000000
χ292222-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-1-1-1000000001111−3−33333−3−3−3−33333−3−3000000000000
χ302222-2-2-2-222-2-2-122-2-2-1-1-1-1-1-1-111111111-2211112i2i−2i−2i2i2i−2i−2i-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii000000000000
χ312222-2-2-2-222-2-2-122-2-2-1-1-1-1-1-1-111111111-221111−2i−2i2i2i−2i−2i2i2i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i000000000000
χ322222-2-2-2-2-2-222-1-2-222-1-11111-11111-1-1-1-1-2211-1-122-2-2-2-222-1-111-1-1-1-111111111-1-1-1-1000000000000
χ332222-2-2-2-2-2-222-1-2-222-1-11111-11111-1-1-1-1-2211-1-1-2-22222-2-2-1-1111111-1-1-1-1-1-1-1-11111000000000000
χ342222-2-2-2-2-2-2-2-22222222-2-2-2-22-2-2-2-222222-222-2-200000000-2-2220000000000000000000000000000
χ352222-2-2-2-2-2-2-2-2-12222-1-11111-11111-1-1-1-12-2-1-1110000000011-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ362222-2-2-2-2-2-2-2-2-12222-1-11111-11111-1-1-1-12-2-1-1110000000011-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ3722-2-22i2i−2i−2i002-222i−2i002-20000-22i2i−2i−2i000000002-22−2−i2i2−i2i22−2002i−2i2−22−2−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ3822-2-22i2i−2i−2i002-222i−2i002-20000-22i2i−2i−2i000000002-2−22i2−i2i2−i2−22002i−2i−22−22i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ3922-2-22i2i−2i−2i002-2-12i−2i00-11−i3−i3i3i31−i−iii33−3−300−i3i3-112−2−i2i2−i2i22−23−3−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ4022-2-22i2i−2i−2i002-2-12i−2i00-11−i3−i3i3i31−i−iii33−3−300−i3i3-11−22i2−i2i2−i2−223−3−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ4122-2-22i2i−2i−2i002-2-12i−2i00-11i3i3−i3−i31−i−iii−3−33300i3−i3-112−2−i2i2−i2i22−2−33−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ4222-2-22i2i−2i−2i002-2-12i−2i00-11i3i3−i3−i31−i−iii−3−33300i3−i3-11−22i2−i2i2−i2−22−33−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ4322-2-22i2i−2i−2i00-222−2i2i002-20000-22i2i−2i−2i00000000-22−i2i2−222−2i2−i200−2i2i−i2i2−i2i2−22−222−22−2i2−i2i2−i2000000000000
χ4422-2-22i2i−2i−2i00-222−2i2i002-20000-22i2i−2i−2i00000000-22i2−i22−2−22−i2i200−2i2ii2−i2i2−i22−22−2−22−22−i2i2−i2i2000000000000
χ4522-2-22i2i−2i−2i00-22-1−2i2i00-11−i3−i3i3i31−i−iii33−3−300i3−i31-1−i2i2−222−2i2−i2−33i−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ4622-2-22i2i−2i−2i00-22-1−2i2i00-11−i3−i3i3i31−i−iii33−3−300i3−i31-1i2−i22−2−22−i2i2−33i−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ4722-2-22i2i−2i−2i00-22-1−2i2i00-11i3i3−i3−i31−i−iii−3−33300−i3i31-1−i2i2−222−2i2−i23−3i−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4822-2-22i2i−2i−2i00-22-1−2i2i00-11i3i3−i3−i31−i−iii−3−33300−i3i31-1i2−i22−2−22−i2i23−3i−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ4922-2-2−2i−2i2i2i002-22−2i2i002-20000-2−2i−2i2i2i000000002-22−2i2−i2i2−i22−200−2i2i2−22−2i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ5022-2-2−2i−2i2i2i002-22−2i2i002-20000-2−2i−2i2i2i000000002-2−22−i2i2−i2i2−2200−2i2i−22−22−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ5122-2-2−2i−2i2i2i002-2-1−2i2i00-11−i3−i3i3i31ii−i−i−3−33300−i3i3-112−2i2−i2i2−i22−2−33i−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5222-2-2−2i−2i2i2i002-2-1−2i2i00-11−i3−i3i3i31ii−i−i−3−33300−i3i3-11−22−i2i2−i2i2−22−33i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5322-2-2−2i−2i2i2i002-2-1−2i2i00-11i3i3−i3−i31ii−i−i33−3−300i3−i3-112−2i2−i2i2−i22−23−3i−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ5422-2-2−2i−2i2i2i002-2-1−2i2i00-11i3i3−i3−i31ii−i−i33−3−300i3−i3-11−22−i2i2−i2i2−223−3i−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ5522-2-2−2i−2i2i2i00-2222i−2i002-20000-2−2i−2i2i2i00000000-22−i2i22−2−22i2−i2002i−2i−i2i2−i2i22−22−2−22−22i2−i2i2−i2000000000000
χ5622-2-2−2i−2i2i2i00-2222i−2i002-20000-2−2i−2i2i2i00000000-22i2−i2−222−2−i2i2002i−2ii2−i2i2−i2−22−222−22−2−i2i2−i2i2000000000000
χ5722-2-2−2i−2i2i2i00-22-12i−2i00-11−i3−i3i3i31ii−i−i−3−33300i3−i31-1−i2i22−2−22i2−i23−3−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5822-2-2−2i−2i2i2i00-22-12i−2i00-11−i3−i3i3i31ii−i−i−3−33300i3−i31-1i2−i2−222−2−i2i23−3−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5922-2-2−2i−2i2i2i00-22-12i−2i00-11i3i3−i3−i31ii−i−i33−3−300−i3i31-1−i2i22−2−22i2−i2−33−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ6022-2-2−2i−2i2i2i00-22-12i−2i00-11i3i3−i3−i31ii−i−i33−3−300−i3i31-1i2−i2−222−2−i2i2−33−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ612-22-22i−2i2i−2i2-2002002i−2i-222-22-2-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ622-22-22i−2i2i−2i2-2002002i−2i-222-22-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ632-22-22i−2i2i−2i-2200200−2i2i-22-22-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ642-22-22i−2i2i−2i-2200200−2i2i-22-22-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ652-22-2−2i2i−2i2i2-200200−2i2i-222-22-2-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ662-22-2−2i2i−2i2i2-200200−2i2i-222-22-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ672-22-2−2i2i−2i2i-22002002i−2i-22-22-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ682-22-2−2i2i−2i2i-22002002i−2i-22-22-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ694-44-44i−4i4i−4i4-400-2004i−4i2-2-22-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i-4400-200−4i4i2-22-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i4-400-200−4i4i2-2-22-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i-4400-2004i−4i2-22-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ734-4-444-4-44000040000-4-4000044-4-4400000000000000000000000000000000000000000000000000
χ744-4-444-4-440000-2000022−2i32i32i3−2i3-2-222-2−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ754-4-444-4-440000-20000222i3−2i3−2i32i3-2-222-22i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ764-4-44-444-4000040000-4-400004-444-400000000000000000000000000000000000000000000000000
χ774-4-44-444-40000-2000022−2i32i32i3−2i3-22-2-222i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ784-4-44-444-40000-20000222i3−2i3−2i32i3-22-2-22−2i32i32i3−2i30000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.