Finite Group Databasebeta

← Group #10690699

Character table — Group #10690699

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222234444444444446661212121266121212121212121212124444888888881212121212121212242424242424242424242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
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χ1011111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
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χ202222222-2-2-2-2-2-22222-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-222-2000000000000
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-1111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ26222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-1111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ27222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-11111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ28222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-11111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ292222-2-2222-2-22222-2-2-2-22222222-2-2-2-222-2-222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ302222-2-2222-2-22222-2-2-2-22222222-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ312222-2-2222-2-2-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000000000002-2-22
χ322222-2-2222-2-2-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000-222-2
χ332222-2-22-2-22222-2-222-2-2222-2-2-2-2-2-222-2-22222-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ342222-2-22-2-22222-2-222-2-2222-2-2-2-2-2-222-2-22222-2-200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ352222-2-22-2-222-2-222-2-2222222222-2-2-2-2-2-222-2-222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ362222-2-22-2-222-2-222-2-2222222222-2-2-2-2-2-222-2-22200000000-222-20000000000000000-2-22222-2-20000000000000000
χ372222-2-2-1-2-22222-2-222-2-2-1-1-1111111-1-111-1-1-1-111000000002i−2i2i−2i−i3−i3i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ382222-2-2-1-2-22222-2-222-2-2-1-1-1111111-1-111-1-1-1-111000000002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ392222-2-2-1-2-22222-2-222-2-2-1-1-1111111-1-111-1-1-1-11100000000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ402222-2-2-1-2-22222-2-222-2-2-1-1-1111111-1-111-1-1-1-11100000000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
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χ422222-2-2-1-2-222-2-222-2-222-1-1-1-1-1-1-1111111-1-111-1-1000000002-2-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ432222-2-2-1-2-222-2-222-2-222-1-1-1-1-1-1-1111111-1-111-1-100000000-222-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ442222-2-2-1-2-222-2-222-2-222-1-1-1-1-1-1-1111111-1-111-1-100000000-222-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ452-22-22-222-22-22i−2i2i−2i2i−2i2i−2i-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ462-22-22-222-22-22i−2i2i−2i2i−2i2i−2i-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ472-22-22-222-22-2−2i2i−2i2i−2i2i−2i2i-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ482-22-22-222-22-2−2i2i−2i2i−2i2i−2i2i-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ492-22-22-22-22-222i−2i−2i2i−2i2i2i−2i-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ502-22-22-22-22-222i−2i−2i2i−2i2i2i−2i-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ512-22-22-22-22-22−2i2i2i−2i2i−2i−2i2i-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ522-22-22-22-22-22−2i2i2i−2i2i−2i−2i2i-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
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χ552-22-22-2-1-22-222i−2i−2i2i−2i2i2i−2i1-11ii−i−i-11i−i1-11-1−ii−ii00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−i3i3−i3i33−33−3−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ562-22-22-2-1-22-222i−2i−2i2i−2i2i2i−2i1-11ii−i−i-11i−i1-11-1−ii−ii00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000i3−i3i3−i3−33−33−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ572-22-22-2-1-22-22−2i2i2i−2i2i−2i−2i2i1-11−i−iii-11−ii1-11-1i−ii−i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−i3i3−i3i3−33−33−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ582-22-22-2-1-22-22−2i2i2i−2i2i−2i−2i2i1-11−i−iii-11−ii1-11-1i−ii−i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000i3−i3i3−i33−33−3−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ592-22-22-2-1-22-22−2i2i2i−2i2i−2i−2i2i1-11−i−iii-11−ii1-11-1i−ii−i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−i3i3−i3i3−33−33ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
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χ622-22-2-2222-2-222i−2i2i−2i−2i2i−2i2i-22-22i2i−2i−2i-22−2i2i2-2-222i−2i−2i2i-22−2i2i00000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ632-22-2-2222-2-22−2i2i−2i2i2i−2i2i−2i-22-2−2i−2i2i2i-222i−2i2-2-22−2i2i2i−2i2-2−2i2i000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ642-22-2-2222-2-22−2i2i−2i2i2i−2i2i−2i-22-2−2i−2i2i2i-222i−2i2-2-22−2i2i2i−2i-222i−2i00000000-222-22i−2i−2i2i00000000000000000000000000000000
χ652-22-2-222-222-22i−2i−2i2i2i−2i−2i2i-22-2−2i−2i2i2i-222i−2i-222-22i−2i−2i2i00000000000000000000000000000000000000002-22i−2i00000000
χ662-22-2-222-222-22i−2i−2i2i2i−2i−2i2i-22-2−2i−2i2i2i-222i−2i-222-22i−2i−2i2i0000000000000000000000000000000000000000-22−2i2i00000000
χ672-22-2-222-222-2−2i2i2i−2i−2i2i2i−2i-22-22i2i−2i−2i-22−2i2i-222-2−2i2i2i−2i00000000000000000000000000000000000000002-2−2i2i00000000
χ682-22-2-222-222-2−2i2i2i−2i−2i2i2i−2i-22-22i2i−2i−2i-22−2i2i-222-2−2i2i2i−2i0000000000000000000000000000000000000000-222i−2i00000000
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χ712-22-2-22-12-2-222i−2i2i−2i−2i2i−2i2i1-11−i−iii1-1i−i-111-1−iii−i-22−2i2i000000001-1-11i−i−ii−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
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χ732-22-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i1-11ii−i−i1-1−ii-111-1i−i−ii2-2−2i2i00000000-111-1i−i−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ742-22-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i1-11ii−i−i1-1−ii-111-1i−i−ii2-2−2i2i00000000-111-1i−i−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ752-22-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i1-11ii−i−i1-1−ii-111-1i−i−ii-222i−2i000000001-1-11−iii−iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ762-22-2-22-12-2-22−2i2i−2i2i2i−2i2i−2i1-11ii−i−i1-1−ii-111-1i−i−ii-222i−2i000000001-1-11−iii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ77444444-2-4-4-4-444-4-4-4-444-2-2-22222-2-2222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ78444444-2-4-4-4-4-4-44444-4-4-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ794444-4-4-244-4-44444-4-4-4-4-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ804444-4-4-244-4-4-4-4-4-44444-2-2-2222222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ814-44-44-4-24-44-44i−4i4i−4i4i−4i4i−4i2-22−2i−2i2i2i-22−2i2i-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ824-44-44-4-24-44-4−4i4i−4i4i−4i4i−4i4i2-222i2i−2i−2i-222i−2i-22-222i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ834-44-4-44-2-444-44i−4i−4i4i4i−4i−4i4i2-222i2i−2i−2i2-2−2i2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ844-44-4-44-2-444-4−4i4i4i−4i−4i4i4i−4i2-22−2i−2i2i2i2-22i−2i2-2-222i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8588-8-80080000000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4000000000000-444−4i34i3−4i34i30000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-4000000000000-4444i3−4i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ888-8-88008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-400000000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800-400000000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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