Finite Group Databasebeta

← Group #69852

Character table — Group #69852

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444422344444466612121212121212121212121244668888888812121212121224242424242424242424242424242424888888882444
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
χ511111111-1-1111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111-1-1111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111-1-1111-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111-1-1111-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
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−i1-11-1
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-11-11
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-11-11
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−iii1-11-1
χ131111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222-2-222-2-2222-2-2-2-22222-2-2-2-2-2-22200000000-2-222-2-20000000000000000000000000000
χ182222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ192222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ202222222222-1-2-222-2-2-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-11133−3−333−3−333−3−333−3−3000000000000
χ212222222222-1-2-222-2-2-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-111−3−333−3−333−3−333−3−333000000000000
χ2222222222-2-22-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222-2-20000000022-2-2220000000000000000000000000000
χ2322222222-2-2-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2112222-2-2-2-2111111-1-1-1-1-1-1-1-111111111000000000000
χ2422222222-2-2-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-2222211111111111111-1-1-1-1-1-1-1-1000000000000
χ2522222222-2-2-1-2-2-2-2-2-2-1-1-11111-1-1-1-11111221100000000-1-111-1-133−3−333−3−3−3−333−3−333000000000000
χ2622222222-2-2-1-2-2-2-2-2-2-1-1-11111-1-1-1-11111221100000000-1-111-1-1−3−333−3−33333−3−333−3−3000000000000
χ272222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-2220000000000000000000000000000
χ282222-2-2-2-222-122-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-12i2i−2i−2i2i2i−2i−2i-1-11111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ292222-2-2-2-222-122-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-1−2i−2i2i2i−2i−2i2i2i-1-11111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ302222-2-2-2-222-1-2-2-2-222-1-1-111111111-1-1-1-1-22-1-1000000001111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ312222-2-2-2-222-1-2-2-2-222-1-1-111111111-1-1-1-1-22-1-1000000001111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ322222-2-2-2-2-2-22-2-22222222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-20000000000000000000000000000
χ332222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-111111111-22112i2i−2i−2i−2i−2i2i2i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ342222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-111111111-2211−2i−2i2i2i2i2i−2i−2i11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ352222-2-2-2-2-2-2-1-2-22222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ362222-2-2-2-2-2-2-1-2-22222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ3722-2-22i−2i2i−2i0022-2002i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ3822-2-22i−2i2i−2i0022-2002i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ3922-2-22i−2i2i−2i002-2200−2i2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ4022-2-22i−2i2i−2i002-2200−2i2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ4122-2-2−2i2i−2i2i0022-200−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ4222-2-2−2i2i−2i2i0022-200−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ4322-2-2−2i2i−2i2i002-22002i−2i2-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ4422-2-2−2i2i−2i2i002-22002i−2i2-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ452-22-22i−2i−2i2i2-22002i−2i00-22-200002i−2i2i−2i0000002-21+i−1−i1−i−1+i1+i−1−i1−i−1+i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ462-22-22i−2i−2i2i2-22002i−2i00-22-200002i−2i2i−2i0000002-2−1−i1+i−1+i1−i−1−i1+i−1+i1−i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ472-22-22i−2i−2i2i2-2-1002i−2i001-113−33−3−ii−ii−i3i3−i3i300-111+i−1−i1−i−1+i1+i−1−i1−i−1+i3−3−ii−i3i3−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ482-22-22i−2i−2i2i2-2-1002i−2i001-113−33−3−ii−ii−i3i3−i3i300-11−1−i1+i−1+i1−i−1−i1+i−1+i1−i3−3−ii−i3i3ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ492-22-22i−2i−2i2i2-2-1002i−2i001-11−33−33−ii−iii3−i3i3−i300-111+i−1−i1−i−1+i1+i−1−i1−i−1+i−33−iii3−i3−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ502-22-22i−2i−2i2i2-2-1002i−2i001-11−33−33−ii−iii3−i3i3−i300-11−1−i1+i−1+i1−i−1−i1+i−1+i1−i−33−iii3−i3ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ512-22-22i−2i−2i2i-22200−2i2i00-22-200002i−2i2i−2i000000-221+i−1−i1−i−1+i−1−i1+i−1+i1−i00−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ522-22-22i−2i−2i2i-22200−2i2i00-22-200002i−2i2i−2i000000-22−1−i1+i−1+i1−i1+i−1−i1−i−1+i00−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ532-22-22i−2i−2i2i-22-100−2i2i001-113−33−3−ii−ii−i3i3−i3i3001-11+i−1−i1−i−1+i−1−i1+i−1+i1−i−33i−ii3−i3−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ542-22-22i−2i−2i2i-22-100−2i2i001-113−33−3−ii−ii−i3i3−i3i3001-1−1−i1+i−1+i1−i1+i−1−i1−i−1+i−33i−ii3−i3ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ552-22-22i−2i−2i2i-22-100−2i2i001-11−33−33−ii−iii3−i3i3−i3001-11+i−1−i1−i−1+i−1−i1+i−1+i1−i3−3i−i−i3i3−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ562-22-22i−2i−2i2i-22-100−2i2i001-11−33−33−ii−iii3−i3i3−i3001-1−1−i1+i−1+i1−i1+i−1−i1−i−1+i3−3i−i−i3i3ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ572-22-2−2i2i2i−2i2-2200−2i2i00-22-20000−2i2i−2i2i0000002-21−i−1+i1+i−1−i1−i−1+i1+i−1−i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ582-22-2−2i2i2i−2i2-2200−2i2i00-22-20000−2i2i−2i2i0000002-2−1+i1−i−1−i1+i−1+i1−i−1−i1+i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ592-22-2−2i2i2i−2i2-2-100−2i2i001-113−33−3i−ii−ii3−i3i3−i300-111−i−1+i1+i−1−i1−i−1+i1+i−1−i3−3i−ii3−i3−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ602-22-2−2i2i2i−2i2-2-100−2i2i001-113−33−3i−ii−ii3−i3i3−i300-11−1+i1−i−1−i1+i−1+i1−i−1−i1+i3−3i−ii3−i3ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ612-22-2−2i2i2i−2i2-2-100−2i2i001-11−33−33i−ii−i−i3i3−i3i300-111−i−1+i1+i−1−i1−i−1+i1+i−1−i−33i−i−i3i3−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ622-22-2−2i2i2i−2i2-2-100−2i2i001-11−33−33i−ii−i−i3i3−i3i300-11−1+i1−i−1−i1+i−1+i1−i−1−i1+i−33i−i−i3i3ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ632-22-2−2i2i2i−2i-222002i−2i00-22-20000−2i2i−2i2i000000-221−i−1+i1+i−1−i−1+i1−i−1−i1+i002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ642-22-2−2i2i2i−2i-222002i−2i00-22-20000−2i2i−2i2i000000-22−1+i1−i−1−i1+i1−i−1+i1+i−1−i002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ652-22-2−2i2i2i−2i-22-1002i−2i001-113−33−3i−ii−ii3−i3i3−i3001-11−i−1+i1+i−1−i−1+i1−i−1−i1+i−33−ii−i3i3−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ662-22-2−2i2i2i−2i-22-1002i−2i001-113−33−3i−ii−ii3−i3i3−i3001-1−1+i1−i−1−i1+i1−i−1+i1+i−1−i−33−ii−i3i3ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ672-22-2−2i2i2i−2i-22-1002i−2i001-11−33−33i−ii−i−i3i3−i3i3001-11−i−1+i1+i−1−i−1+i1−i−1−i1+i3−3−iii3−i3−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ682-22-2−2i2i2i−2i-22-1002i−2i001-11−33−33i−ii−i−i3i3−i3i3001-1−1+i1−i−1−i1+i1−i−1+i1+i−1−i3−3−iii3−i3ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ6944-4-44i−4i4i−4i00-24-4004i−4i-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ7044-4-44i−4i4i−4i00-2-4400−4i4i-22222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i00-24-400−4i4i-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ7244-4-4−4i4i−4i4i00-2-44004i−4i-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ734-4-4444-4-4004000000-4-4400004-4-4400000000000000000000000000000000000000000000000000
χ744-4-4444-4-400-200000022-223−23−2323-222-2−232323−230000000000000000000000000000000000000000000000
χ754-4-4444-4-400-200000022-2−232323−23-222-223−23−23230000000000000000000000000000000000000000000000
χ764-4-44-4-444004000000-4-440000-444-400000000000000000000000000000000000000000000000000
χ774-4-44-4-44400-200000022-223−23−23232-2-2223−23−23230000000000000000000000000000000000000000000000
χ784-4-44-4-44400-200000022-2−232323−232-2-22−232323−230000000000000000000000000000000000000000000000

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