Finite Group Databasebeta

← Group #69443

Character table — Group #69443

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444422223444466666661212121212121212244444444466661212121212121212121212121212121212121212888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i1-1-11
χ611111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−i−i−iiiii-111-1
χ711111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1iiii−i−i−i−i-111-1
χ811111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii1-1-11
χ91111-1-1-1-111-1-1111-1-111-1-1-1-11-1-1-1-11111-11ii−i−iii−i−i-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1111-1-111-1-1-1-11-1-1-1-11111-11ii−i−iii−i−i-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1111-1-111-1-1-1-11-1-1-1-11111-11−i−iii−i−iii-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i-1-111
χ121111-1-1-1-111-1-1111-1-111-1-1-1-11-1-1-1-11111-11−i−iii−i−iii-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ131111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-11-1
χ141111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-11
χ151111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-11-11
χ161111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11-11-1
χ17222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ18222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-1000000000000
χ192222222222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-200000000-2-2220000000000000000-2-222000000000000
χ202222222222-2-2-1-2-222-1-11111-1-1-1-1-11111-2-20000000011-1-133−3−333−3−333−3−333−3−311-1-1000000000000
χ212222222222-2-2-1-2-222-1-11111-1-1-1-1-11111-2-20000000011-1-1−3−333−3−333−3−333−3−33311-1-1000000000000
χ2222222222-2-222222-2-2222222222222222-2-200000000-2-2-2-20000000000000000-2-2-2-2000000000000
χ2322222222-2-222-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000001111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i31111000000000000
χ2422222222-2-222-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000001111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i31111000000000000
χ2522222222-2-2-2-2-1-2-2-2-2-1-11111-1-1-1-1-11111222i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-111000000000000
χ2622222222-2-2-2-2-1-2-2-2-2-1-11111-1-1-1-1-1111122−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-111000000000000
χ272222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-22-20000000022220000000000000000-2-2-2-2000000000000
χ282222-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1111111112-200000000-1-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i31111000000000000
χ292222-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1111111112-200000000-1-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i31111000000000000
χ302222-2-2-2-222-2-2-122-2-2-1-11111-11111-1-1-1-1-222i2i−2i−2i2i2i−2i−2i11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111000000000000
χ312222-2-2-2-222-2-2-122-2-2-1-11111-11111-1-1-1-1-22−2i−2i2i2i−2i−2i2i2i11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111000000000000
χ322222-2-2-2-2-2-222-1-2-222-1-1-1-1-1-1-111111111-2222-2-2-2-2221111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ332222-2-2-2-2-2-222-1-2-222-1-1-1-1-1-1-111111111-22-2-22222-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-1000000000000
χ342222-2-2-2-2-2-2-2-22222222-2-2-2-22-2-2-2-222222-20000000022-2-20000000000000000-2-222000000000000
χ352222-2-2-2-2-2-2-2-2-12222-1-11111-11111-1-1-1-12-200000000-1-11133−3−3−3−333−3−33333−3−311-1-1000000000000
χ362222-2-2-2-2-2-2-2-2-12222-1-11111-11111-1-1-1-12-200000000-1-111−3−33333−3−333−3−3−3−33311-1-1000000000000
χ3722-2-22i2i−2i−2i002-222i−2i002-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000002−2−i2i2−i2i22−20000
χ3822-2-22i2i−2i−2i002-222i−2i002-222-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000−22i2−i2i2−i2−220000
χ3922-2-22i2i−2i−2i00-222−2i2i002-2-2-222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000−i2i2−222−2i2−i20000
χ4022-2-22i2i−2i−2i00-222−2i2i002-2-2-222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000i2−i22−2−22−i2i20000
χ4122-2-2−2i−2i2i2i002-22−2i2i002-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000002−2i2−i2i2−i22−20000
χ4222-2-2−2i−2i2i2i002-22−2i2i002-222-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000−22−i2i2−i2i2−220000
χ4322-2-2−2i−2i2i2i00-2222i−2i002-2-2-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000−i2i22−2−22i2−i20000
χ4422-2-2−2i−2i2i2i00-2222i−2i002-2-2-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000i2−i2−222−2−i2i20000
χ452-22-22i−2i2i−2i2-2002002i−2i-220000-22i−2i2i−2i0000001+i−1−i1−i−1+i1+i−1−i1−i−1+i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i000000000000
χ462-22-22i−2i2i−2i2-2002002i−2i-220000-22i−2i2i−2i000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i000000000000
χ472-22-22i−2i2i−2i2-200-1002i−2i1-1−i3i3−i3i31−ii−ii3−33−3001+i−1−i1−i−1+i1+i−1−i1−i−1+i−i3i3-11−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ143−3−ii000000000000
χ482-22-22i−2i2i−2i2-200-1002i−2i1-1−i3i3−i3i31−ii−ii3−33−300−1−i1+i−1+i1−i−1−i1+i−1+i1−i−i3i3-11ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ143−3−ii000000000000
χ492-22-22i−2i2i−2i2-200-1002i−2i1-1i3−i3i3−i31−ii−ii−33−33001+i−1−i1−i−1+i1+i−1−i1−i−1+ii3−i3-11−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−33−ii000000000000
χ502-22-22i−2i2i−2i2-200-1002i−2i1-1i3−i3i3−i31−ii−ii−33−3300−1−i1+i−1+i1−i−1−i1+i−1+i1−ii3−i3-11ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−33−ii000000000000
χ512-22-22i−2i2i−2i-2200200−2i2i-220000-22i−2i2i−2i0000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00-221−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i00−2i2i000000000000
χ522-22-22i−2i2i−2i-2200200−2i2i-220000-22i−2i2i−2i000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00-22−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i00−2i2i000000000000
χ532-22-22i−2i2i−2i-2200-100−2i2i1-1−i3i3−i3i31−ii−ii3−33−3001−i−1+i−1−i1+i−1+i1−i1+i−1−ii3−i31-1−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−33i−i000000000000
χ542-22-22i−2i2i−2i-2200-100−2i2i1-1−i3i3−i3i31−ii−ii3−33−300−1+i1−i1+i−1−i1−i−1+i−1−i1+ii3−i31-1ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−33i−i000000000000
χ552-22-22i−2i2i−2i-2200-100−2i2i1-1i3−i3i3−i31−ii−ii−33−33001−i−1+i−1−i1+i−1+i1−i1+i−1−i−i3i31-1−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ223−3i−i000000000000
χ562-22-22i−2i2i−2i-2200-100−2i2i1-1i3−i3i3−i31−ii−ii−33−3300−1+i1−i1+i−1−i1−i−1+i−1−i1+i−i3i31-1ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ223−3i−i000000000000
χ572-22-2−2i2i−2i2i2-200200−2i2i-220000-2−2i2i−2i2i0000001−i−1+i1+i−1−i1−i−1+i1+i−1−i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i000000000000
χ582-22-2−2i2i−2i2i2-200200−2i2i-220000-2−2i2i−2i2i000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i000000000000
χ592-22-2−2i2i−2i2i2-200-100−2i2i1-1−i3i3−i3i31i−ii−i−33−33001−i−1+i1+i−1−i1−i−1+i1+i−1−i−i3i3-11−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−33i−i000000000000
χ602-22-2−2i2i−2i2i2-200-100−2i2i1-1−i3i3−i3i31i−ii−i−33−3300−1+i1−i−1−i1+i−1+i1−i−1−i1+i−i3i3-11ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−33i−i000000000000
χ612-22-2−2i2i−2i2i2-200-100−2i2i1-1i3−i3i3−i31i−ii−i3−33−3001−i−1+i1+i−1−i1−i−1+i1+i−1−ii3−i3-11−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ223−3i−i000000000000
χ622-22-2−2i2i−2i2i2-200-100−2i2i1-1i3−i3i3−i31i−ii−i3−33−300−1+i1−i−1−i1+i−1+i1−i−1−i1+ii3−i3-11ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ223−3i−i000000000000
χ632-22-2−2i2i−2i2i-22002002i−2i-220000-2−2i2i−2i2i0000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00-221+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i002i−2i000000000000
χ642-22-2−2i2i−2i2i-22002002i−2i-220000-2−2i2i−2i2i000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00-22−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i002i−2i000000000000
χ652-22-2−2i2i−2i2i-2200-1002i−2i1-1−i3i3−i3i31i−ii−i−33−33001+i−1−i−1+i1−i−1−i1+i1−i−1+ii3−i31-1−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ143−3−ii000000000000
χ662-22-2−2i2i−2i2i-2200-1002i−2i1-1−i3i3−i3i31i−ii−i−33−3300−1−i1+i1−i−1+i1+i−1−i−1+i1−ii3−i31-1ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ143−3−ii000000000000
χ672-22-2−2i2i−2i2i-2200-1002i−2i1-1i3−i3i3−i31i−ii−i3−33−3001+i−1−i−1+i1−i−1−i1+i1−i−1+i−i3i31-1−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−33−ii000000000000
χ682-22-2−2i2i−2i2i-2200-1002i−2i1-1i3−i3i3−i31i−ii−i3−33−300−1−i1+i1−i−1+i1+i−1−i−1+i1−i−i3i31-1ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−33−ii000000000000
χ6944-4-44i4i−4i−4i004-4-24i−4i00-22-2-2222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ7044-4-44i4i−4i−4i00-44-2−4i4i00-2222-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ7144-4-4−4i−4i4i4i004-4-2−4i4i00-22-2-22222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ7244-4-4−4i−4i4i4i00-44-24i−4i00-2222-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000
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.