Finite Group Databasebeta

← Group #10690734

Character table — Group #10690734

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212124444888888881212121212121212242424242424242424242424242424242444444488888888
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
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−i−iiiii−i−i
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χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ25222222-2-2-2-222222-2-2-2-22222222-2-2-2-222-2-222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ26222222-2-2-2-222222-2-2-2-22222222-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ27222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000000000002-2-22
χ28222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000-222-2
χ292222-2-222-2-2222-2-222-2-22-2-2-2-22222-2-22222-2-2-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
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χ312222-2-222-2-22-2-222-2-2222-2-2-2-22222-2-2-2-2-2-22222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ322222-2-222-2-22-2-222-2-2222-2-2-2-22222-2-2-2-2-2-2222200000000-222-20000000000000000-2-22222-2-20000000000000000
χ332222-2-222-2-2-122-2-222-2-2-11111-1-1-1-111-1-1-1-11111000000002i−2i2i−2i−i3−i3i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ342222-2-222-2-2-122-2-222-2-2-11111-1-1-1-111-1-1-1-11111000000002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ352222-2-222-2-2-122-2-222-2-2-11111-1-1-1-111-1-1-1-1111100000000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ362222-2-222-2-2-122-2-222-2-2-11111-1-1-1-111-1-1-1-1111100000000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ372222-2-222-2-2-1-2-222-2-222-11111-1-1-1-1111111-1-1-1-1000000002-2-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ382222-2-222-2-2-1-2-222-2-222-11111-1-1-1-1111111-1-1-1-1000000002-2-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ392222-2-222-2-2-1-2-222-2-222-11111-1-1-1-1111111-1-1-1-100000000-222-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ402222-2-222-2-2-1-2-222-2-222-11111-1-1-1-1111111-1-1-1-100000000-222-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ412222-2-2-2-222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-2220000000000000000000000000000000000002-2-22000000000000
χ422222-2-2-2-222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-222000000000000000000000000000000000000-222-2000000000000
χ432222-2-2-2-2222-2-22222-2-22-2-2-2-222-2-222-2-22222-2-200000000000000000000000000000000000022-2-2000000000000
χ442222-2-2-2-2222-2-22222-2-22-2-2-2-222-2-222-2-22222-2-2000000000000000000000000000000000000-2-222000000000000
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χ462-22-22-22-22-222i−2i2i−2i2i−2i2i−2i-222-2-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ472-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i-222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ482-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i-222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ492-22-22-2-22-2222i−2i2i−2i−2i2i−2i2i-222-2-22-2-22-222i−2i−2i2i2i−2i−2i2i2-22i−2i000000002-22-22i−2i2i−2i00000000000000000000000000000000
χ502-22-22-2-22-2222i−2i2i−2i−2i2i−2i2i-222-2-22-2-22-222i−2i−2i2i2i−2i−2i2i-22−2i2i00000000-22-22−2i2i−2i2i00000000000000000000000000000000
χ512-22-22-2-22-222−2i2i−2i2i2i−2i2i−2i-222-2-22-2-22-22−2i2i2i−2i−2i2i2i−2i2-2−2i2i000000002-22-2−2i2i−2i2i00000000000000000000000000000000
χ522-22-22-2-22-222−2i2i−2i2i2i−2i2i−2i-222-2-22-2-22-22−2i2i2i−2i−2i2i2i−2i-222i−2i00000000-22-222i−2i2i−2i00000000000000000000000000000000
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χ542-22-22-2-22-22-12i−2i2i−2i−2i2i−2i2i1-1-111-111-11-1−iii−i−iii−i2-22i−2i00000000-11-11−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ552-22-22-2-22-22-12i−2i2i−2i−2i2i−2i2i1-1-111-111-11-1−iii−i−iii−i-22−2i2i000000001-11-1i−ii−i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
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χ572-22-22-2-22-22-1−2i2i−2i2i2i−2i2i−2i1-1-111-111-11-1i−i−iii−i−ii2-2−2i2i00000000-11-11i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ582-22-22-2-22-22-1−2i2i−2i2i2i−2i2i−2i1-1-111-111-11-1i−i−iii−i−ii2-2−2i2i00000000-11-11i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ592-22-22-2-22-22-1−2i2i−2i2i2i−2i2i−2i1-1-111-111-11-1i−i−iii−i−ii-222i−2i000000001-11-1−ii−iiζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
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χ632-22-2-222-2-222−2i2i2i−2i−2i2i2i−2i-2-2-2222-22-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000002-2−2i2i00000000
χ642-22-2-222-2-222−2i2i2i−2i−2i2i2i−2i-2-2-2222-22-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000-222i−2i00000000
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χ732-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−i3i3i3−i3−333−3−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ742-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000i3−i3−i3i33−3−33−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ752-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−i3i3i3−i3−333−3ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ762-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i111-1-1-111-1-11i−i−ii−iii−i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000i3−i3−i3i33−3−33ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ77444444-4-4-4-4-24444-4-4-4-4-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ78444444-4-4-4-4-2-4-4-4-44444-2-2-2-2-2-2-2222222-2-222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-244-4-4-4-444-22222-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-4-44444-4-4-22222-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ814-44-44-44-44-4-24i−4i4i−4i4i−4i4i−4i2-2-222-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ824-44-44-44-44-4-2−4i4i−4i4i−4i4i−4i4i2-2-222-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ834-44-4-444-4-44-24i−4i−4i4i4i−4i−4i4i222-2-2-22-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ844-44-4-444-4-44-2−4i4i4i−4i−4i4i4i−4i222-2-2-22-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ8588-8-800000080000000080000-8-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000-4−4i34i3−4i34i3440000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-400000000-44i3−4i34i3−4i3440000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-80000-880000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004−4i34i34i3−4i34-40000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-40000000044i3−4i3−4i34i34-40000000000000000000000000000000000000000000000000000000000000000

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