Finite Group Databasebeta

← Group #13156368

Character table — Group #13156368

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order1222333446666666661212121233366666666612121212121212121212121244366612121212121248812121212121212121212121212121212242424242424242424242424242424244121212121212121244882424242441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ71111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-20022-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2200-2-222-2-222-2-2-2-222220000000000000000000000000000000000000000
χ11222222-12222-1222-12-122222-1-122-12-1-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-12002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000222-1-1-1-1-1-100000000200-1-100
χ12222222-12222-1222-12-122222-1-122-12-1-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-12002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-211111100000000-2001100
χ13222222-12222-1222-12-122222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-2-2-21111111111110000000000000000222-1-1-1-1-1-100000000-2001100
χ14222222-12222-1222-12-122222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-2-2-21111111111110000000000000000-2-2-211111100000000200-1-100
χ15222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-20022-2-2-1-111-1-1-1-111110000000000000000000−i3i3−i3−i3i3i300000000000−i3i300
χ16222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-20022-2-2-1-111-1-1-1-111110000000000000000000i3−i3i3i3−i3−i300000000000i3−i300
χ17222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111200-2-22211-1-11111-1-1-1-10000000000000000000−i3i3−i3−i3i3i300000000000i3−i300
χ18222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111200-2-22211-1-11111-1-1-1-10000000000000000000i3−i3i3i3−i3−i300000000000−i3i300
χ1922222-12222-1222-12-122222-12-1-1-1-1-12-122-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1220000000-1-10000
χ2022222-12222-1222-12-122222-12-1-1-1-1-12-122-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-21111-2-20000000110000
χ2122222-12222-1222-12-122222-12-1-1-1-1-12-122-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-21111111111112-1-122-1-1-1-1-2-20000000110000
χ2222222-12222-1222-12-122222-12-1-1-1-1-12-122-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-2111111111111-211-2-21111220000000-1-10000
χ232222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000022-1-1-1-10000000
χ242222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-2-2-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000000-2-211110000000
χ252222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-2221111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000000-2-211110000000
χ262222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-2-2-21111-2-2-2-2111111111111-2-2-2-2111111110000000000022-1-1-1-10000000
χ272222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-1-1-1-1-2-21111-200-1-11122-2-2-1-1-1-1111133−3−300003333−3−3−3−3000000000000033−3−30000000
χ282222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-1-1-1-1-2-21111-200-1-11122-2-2-1-1-1-11111−3−3330000−3−3−3−333330000000000000−3−3330000000
χ292222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-1-1-2-2221111-1-1-1-133−3−300003333−3−3−3−30000000000000−3−3330000000
χ302222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-1-1-2-2221111-1-1-1-1−3−3330000−3−3−3−33333000000000000033−3−30000000
χ312-22-222200-2-2-22-2-2-22200002222-22-2-2-22-2-20000000000002i−2i22-2-20000000−i2i22i−2i002i−2i002i2i−2i−2i0000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000002−22−22−20000000
χ322-22-222200-2-2-22-2-2-22200002222-22-2-2-22-2-20000000000002i−2i22-2-20000000i2−i22i−2i002i−2i002i2i−2i−2i0000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000−22−22−220000000
χ332-22-222200-2-2-22-2-2-22200002222-22-2-2-22-2-2000000000000−2i2i22-2-20000000−i2i2−2i2i00−2i2i00−2i−2i2i2i0000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000−22−22−220000000
χ342-22-222200-2-2-22-2-2-22200002222-22-2-2-22-2-2000000000000−2i2i22-2-20000000i2−i2−2i2i00−2i2i00−2i−2i2i2i0000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000002−22−22−20000000
χ352-22-2-122001-2-2-11-2-2223−33−3-1-12-11211-2-11-20003−333−3−303−32i−2i-1-1110033−3−30−i2i2−ii−i3i32i−2i00−i−iii−i3−i3i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ362-22-2-122001-2-2-11-2-2223−33−3-1-12-11211-2-11-20003−333−3−303−32i−2i-1-1110033−3−30i2−i2−ii−i3i32i−2i00−i−iii−i3−i3i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ372-22-2-122001-2-2-11-2-2223−33−3-1-12-11211-2-11-20003−333−3−303−3−2i2i-1-1110033−3−30−i2i2i−ii3−i3−2i2i00ii−i−ii3i3−i3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ382-22-2-122001-2-2-11-2-2223−33−3-1-12-11211-2-11-20003−333−3−303−3−2i2i-1-1110033−3−30i2−i2i−ii3−i3−2i2i00ii−i−ii3i3−i3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ392-22-2-122001-2-2-11-2-222−33−33-1-12-11211-2-11-2000−33−3−3330−332i−2i-1-11100−3−3330−i2i2−iii3−i32i−2i00−i−iiii3i3−i3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ402-22-2-122001-2-2-11-2-222−33−33-1-12-11211-2-11-2000−33−3−3330−332i−2i-1-11100−3−3330i2−i2−iii3−i32i−2i00−i−iiii3i3−i3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ412-22-2-122001-2-2-11-2-222−33−33-1-12-11211-2-11-2000−33−3−3330−33−2i2i-1-11100−3−3330−i2i2i−i−i3i3−2i2i00ii−i−i−i3−i3i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ422-22-2-122001-2-2-11-2-222−33−33-1-12-11211-2-11-2000−33−3−3330−33−2i2i-1-11100−3−3330i2−i2i−i−i3i3−2i2i00ii−i−i−i3−i3i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ432-2-222222-2222-2-2-2-2-2-222-2-2222-2-2-2222-2-2-222-2222-22-2-2-2-2002-2-222-22-22-20000000000000000000000000000000000000000000000000000000002-2
χ442-2-222222-2222-2-2-2-2-2-222-2-2222-2-2-2222-2-2-222-2222-22-2-2-2-2002-2-222-22-22-2000000000000000000000000000000000000000000000000000000000-22
χ452-2-22222-22222-2-2-2-2-2-2-2-222222-2-2-2222-2-2-2-2-22-2-2-22-22222002-2-22-22-22-22000000000000000000000000000000000000000000002i−2i00000002i−2i0000
χ462-2-22222-22222-2-2-2-2-2-2-2-222222-2-2-2222-2-2-2-2-22-2-2-22-22222002-2-22-22-22-2200000000000000000000000000000000000000000000−2i2i0000000−2i2i0000
χ472-2-222-12-222-12-2-21-21-2-2-222-12-1111-12-1-2-211-2211-22-22-1-1-100-111-11-11-11-100000000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i303−3003−33−32i−2i0000000−ii0000
χ482-2-222-12-222-12-2-21-21-2-2-222-12-1111-12-1-2-211-2211-22-22-1-1-100-111-11-11-11-100000000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30−3300−33−33−2i2i0000000i−i0000
χ492-2-222-12-222-12-2-21-21-2-2-222-12-1111-12-1-2-211-2211-22-22-1-1-100-111-11-11-11-100000000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i303−3003−33−3−2i2i0000000i−i0000
χ502-2-222-12-222-12-2-21-21-2-2-222-12-1111-12-1-2-211-2211-22-22-1-1-100-111-11-11-11-100000000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30−3300−33−332i−2i0000000−ii0000
χ5144444-24-4-44-2444-24-24-4-4-4-4-24-2-2-2-2-24-244-22-4-422-4-4-4-422200-2-2-2-222222200000000000000000000000000000000000000000000000000000000000
χ5244444-2-2444-2-244-2-2-2-24444-2-21-2-21-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-2001111111111000000000000000000000000000000000004-2-2-2-21111000000000000000
χ5344444-2-2444-2-244-2-2-2-24444-2-21-2-21-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-200111111111100000000000000000000000000000000000-42222-1-1-1-1000000000000000
χ5444444-2-2-4-44-2-244-2-2-2-2-4-4-4-4-2-21-2-21-2-21-2-21222222222222001111-1-1-1-1-1-100000000000000000000000000000000000000−2i32i3i3i3−i3−i3000000000000000
χ5544444-2-2-4-44-2-244-2-2-2-2-4-4-4-4-2-21-2-21-2-21-2-21222222222222001111-1-1-1-1-1-1000000000000000000000000000000000000002i3−2i3−i3−i3i3i3000000000000000
χ564444-24-244-24-2-2-24-24-2-2-2-2-2-21-2-2-2-2-21-211-24-2-2-2-211114-2-2441111-2-21111400-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000000000
χ574444-24-244-24-2-2-24-24-2-2-2-2-2-21-2-2-2-2-21-211-24-2-2-2-211114-2-2-4-41111-2-21111-40022222222-1-1-1-1-1-1-1-10000000000000000000000000000000000000000
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χ594444-24-2-4-4-24-2-2-24-24-22222-21-2-2-2-2-21-211-2-42222-1-1-1-1-422-4-4111122-1-1-1-140022-2-222-2-2-1-1-1-111110000000000000000000000000000000000000000
χ604444-2-2444-2-24-2-2-24-24-2-2-2-21-2-211-21-2-2-2-2-2-24411-2-2-2-2-211001111-2-211110440000000000000000-2-2-2-2-2-2-2-211111111000000000000000000000000
χ614444-2-2444-2-24-2-2-24-24-2-2-2-21-2-211-21-2-2-2-2-2-24411-2-2-2-2-211001111-2-211110-4-4000000000000000022222222-1-1-1-1-1-1-1-1000000000000000000000000
χ624444-2-24-4-4-2-24-2-2-24-2422221-2-211-21-2-2-2-2-22-4-4-1-122222-1-100111122-1-1-1-100000000000000000002323−23−230000−3−3−3−33333000000000000000000000000
χ634444-2-24-4-4-2-24-2-2-24-2422221-2-211-21-2-2-2-2-22-4-4-1-122222-1-100111122-1-1-1-10000000000000000000−23−23232300003333−3−3−3−3000000000000000000000000
χ6444-4-444400-4-4-4-4444-4-40000444-44-4-4-4-4-444000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
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χ6944-4-4-244002-4-42-244-4-423−23−2323-2-242-2-422-42-2400023−2323−23−23230−232300-22-220023−23−232300000000000000000000000000000000000000000000000000000000000
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χ7144-4-4-24-2002-422-24-2-4223−23−2323-21-22-222-12-11-200023−23−333−30−2323001-11-100−333−300000000023−233-33-3−33−330000000000000000000000000000000000000000
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χ7344-4-4-24-2002-422-24-2-42−232323−23-21-22-222-12-11-2000−23233−3−33023−23001-11-1003−3−3300000000023−23-33-33−33−330000000000000000000000000000000000000000
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χ984-4-44-2444-4-24422-4-4-4-4-2-222-2-2422-4-2-2422-444-4-2-2-22-22-42200-222-24-4-22-2200000000000000000000000000000000000000000000000000000000000
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χ1178-8-88-4-4-4-88-4-4-444444444-4-4222-2-2-2222-2-2-244-4-2-2-22-22-42200-111-1-221-11-100000000000000000000000000000000000000000000000000000000000

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