Finite Group Databasebeta

← Group #69853

Character table — Group #69853

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444434444444466612121212121212121212121224668888888812121212121224242424242424242424242424242424888888882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11-111ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-1-11
χ101111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11-111ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-111-1
χ111111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11-111−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-111-1
χ121111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11-111−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-1-11
χ131111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1
χ141111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-111
χ151111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-111
χ161111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1
χ17222222222-2-22222-2-2222-2-2-2-22222-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000
χ18222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-2222200000000-2-2-2-2220000000000000000000000000000
χ1922222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2022222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ2122222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2112222-2-2-2-2111111-1-1-1-1-1-1-1-111111111000000000000
χ2222222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-2222211111111111111-1-1-1-1-1-1-1-1000000000000
χ2322222222-1-2-22222-2-2-1-1-11111-1-1-1-11111-2-21100000000-1-1-1-11133−3−333−3−333−3−333−3−3000000000000
χ2422222222-1-2-22222-2-2-1-1-11111-1-1-1-11111-2-21100000000-1-1-1-111−3−333−3−333−3−333−3−333000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1111122-1-1000000001111-1-133−3−333−3−3−3−333−3−333000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1111122-1-1000000001111-1-1−3−333−3−33333−3−333−3−3000000000000
χ272222-2-2-2-22-2-222-2-222222-2-2-2-2-2-2-2-22222-22-2-20000000022-2-2220000000000000000000000000000
χ282222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-222222-22200000000-2-222-2-20000000000000000000000000000
χ292222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-12i2i−2i−2i2i2i−2i−2i-1-11111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ302222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-1−2i−2i2i2i−2i−2i2i2i-1-11111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ312222-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-22112i2i−2i−2i−2i−2i2i2i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ322222-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-2211−2i−2i2i2i2i2i−2i−2i11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ332222-2-2-2-2-1-2-222-2-222-1-1-111111111-1-1-1-1-221100000000-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ342222-2-2-2-2-1-2-222-2-222-1-1-111111111-1-1-1-1-221100000000-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ352222-2-2-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-12-2-1-10000000011-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ362222-2-2-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-12-2-1-10000000011-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ3722-2-22i2i−2i−2i2002i−2i2-2002-2-200002i2i−2i−2i000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i2i−2i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3822-2-22i2i−2i−2i2002i−2i2-2002-2-200002i2i−2i−2i00000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i2i−2i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3922-2-22i2i−2i−2i200−2i2i-22002-2-200002i2i−2i−2i000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i−2i2i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4022-2-22i2i−2i−2i200−2i2i-22002-2-200002i2i−2i−2i00000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i−2i2i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4122-2-22i2i−2i−2i-1002i−2i2-200-11133−3−3−i−iii−i3−i3i3i300−i3i31+i−1−i1−i−1+i1−i−1+i1+i−1−i−ii-113−3−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ4222-2-22i2i−2i−2i-1002i−2i2-200-11133−3−3−i−iii−i3−i3i3i300−i3i3−1−i1+i−1+i1−i−1+i1−i−1−i1+i−ii-113−3ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ4322-2-22i2i−2i−2i-1002i−2i2-200-111−3−333−i−iiii3i3−i3−i300i3−i31+i−1−i1−i−1+i1−i−1+i1+i−1−i−ii-11−33−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ4422-2-22i2i−2i−2i-1002i−2i2-200-111−3−333−i−iiii3i3−i3−i300i3−i3−1−i1+i−1+i1−i−1+i1−i−1−i1+i−ii-11−33ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ4522-2-22i2i−2i−2i-100−2i2i-2200-11133−3−3−i−iii−i3−i3i3i300i3−i31+i−1−i1−i−1+i−1+i1−i−1−i1+ii−i1-1−33−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ4622-2-22i2i−2i−2i-100−2i2i-2200-11133−3−3−i−iii−i3−i3i3i300i3−i3−1−i1+i−1+i1−i1−i−1+i1+i−1−ii−i1-1−33ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ4722-2-22i2i−2i−2i-100−2i2i-2200-111−3−333−i−iiii3i3−i3−i300−i3i31+i−1−i1−i−1+i−1+i1−i−1−i1+ii−i1-13−3−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ4822-2-22i2i−2i−2i-100−2i2i-2200-111−3−333−i−iiii3i3−i3−i300−i3i3−1−i1+i−1+i1−i1−i−1+i1+i−1−ii−i1-13−3ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ4922-2-2−2i−2i2i2i2002i−2i-22002-2-20000−2i−2i2i2i000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i2i−2i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ5022-2-2−2i−2i2i2i2002i−2i-22002-2-20000−2i−2i2i2i00000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i2i−2i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ5122-2-2−2i−2i2i2i200−2i2i2-2002-2-20000−2i−2i2i2i000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i−2i2i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ5222-2-2−2i−2i2i2i200−2i2i2-2002-2-20000−2i−2i2i2i00000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i−2i2i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ5322-2-2−2i−2i2i2i-1002i−2i-2200-11133−3−3ii−i−ii3i3−i3−i300−i3i31−i−1+i1+i−1−i−1−i1+i−1+i1−i−ii1-1−33−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ5422-2-2−2i−2i2i2i-1002i−2i-2200-11133−3−3ii−i−ii3i3−i3−i300−i3i3−1+i1−i−1−i1+i1+i−1−i1−i−1+i−ii1-1−33ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ5522-2-2−2i−2i2i2i-1002i−2i-2200-111−3−333ii−i−i−i3−i3i3i300i3−i31−i−1+i1+i−1−i−1−i1+i−1+i1−i−ii1-13−3−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ5622-2-2−2i−2i2i2i-1002i−2i-2200-111−3−333ii−i−i−i3−i3i3i300i3−i3−1+i1−i−1−i1+i1+i−1−i1−i−1+i−ii1-13−3ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ5722-2-2−2i−2i2i2i-100−2i2i2-200-11133−3−3ii−i−ii3i3−i3−i300i3−i31−i−1+i1+i−1−i1+i−1−i1−i−1+ii−i-113−3−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ5822-2-2−2i−2i2i2i-100−2i2i2-200-11133−3−3ii−i−ii3i3−i3−i300i3−i3−1+i1−i−1−i1+i−1−i1+i−1+i1−ii−i-113−3ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ5922-2-2−2i−2i2i2i-100−2i2i2-200-111−3−333ii−i−i−i3−i3i3i300−i3i31−i−1+i1+i−1−i1+i−1−i1−i−1+ii−i-11−33−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ6022-2-2−2i−2i2i2i-100−2i2i2-200-111−3−333ii−i−i−i3−i3i3i300−i3i3−1+i1−i−1−i1+i−1−i1+i−1+i1−ii−i-11−33ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ612-22-22i−2i2i−2i22-200002i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ622-22-22i−2i2i−2i22-200002i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ632-22-22i−2i2i−2i2-220000−2i2i-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ642-22-22i−2i2i−2i2-220000−2i2i-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ652-22-2−2i2i−2i2i22-20000−2i2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ662-22-2−2i2i−2i2i22-20000−2i2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ672-22-2−2i2i−2i2i2-2200002i−2i-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ682-22-2−2i2i−2i2i2-2200002i−2i-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ694-44-44i−4i4i−4i-24-400004i−4i2-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i-2-440000−4i4i2-222-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i-24-40000−4i4i2-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i-2-4400004i−4i2-222-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ734-4-444-4-44400000000-4-4400004-4-4400000000000000000000000000000000000000000000000000
χ744-4-444-4-44-20000000022-223−23−2323-222-2−232323−230000000000000000000000000000000000000000000000
χ754-4-444-4-44-20000000022-2−232323−23-222-223−23−23230000000000000000000000000000000000000000000000
χ764-4-44-444-4400000000-4-440000-444-400000000000000000000000000000000000000000000000000
χ774-4-44-444-4-20000000022-223−23−23232-2-2223−23−23230000000000000000000000000000000000000000000000
χ784-4-44-444-4-20000000022-2−232323−232-2-22−232323−230000000000000000000000000000000000000000000000

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