Finite Group Databasebeta

← Group #10690505

Character table — Group #10690505

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order1222444434444444466612121212248888121212121212121268888881224242424242424242424242424242424888888888888246612122244888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−i1111-1-1-1-1-1i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-11-111-1-111-1-1i−iii−i−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−i1111-1-1-1-1-1i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1-1-111111-111-1-1-1-111−ii−i−iii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−i1111-1-1-1-1-1i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-1-1-11111-11-1-11111-1-1i−i−i−iii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−i1111-1-1-1-1-1i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii−i−iii1111-1-1-1-1-11-1-111-1-111−iiii−i−i
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iii1111-1-1-1-1-1−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−iii−i−i1111-1-1-1-1-11-1-111-1-111i−i−i−iii
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iii1111-1-1-1-1-1−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-1-1-11111-11-1-11111-1-1−iiii−i−i
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iii1111-1-1-1-1-1−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1-1-111111-111-1-1-1-111i−iii−i−i
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iii1111-1-1-1-1-1−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii−i−iii1111-1-1-1-11-111-1-111-1-1−ii−i−iii
χ1722222222222-2-222-2-22222222-2-2222222-2-2-2-222-2-2-20000-222-2-222-2-2000000000000000000000000000000000000
χ1822222222222-2-222-2-22222222-2-2-2-2-2-222-2-2-2-222-2220000-2-2-222-2-222000000000000000000000000000000000000
χ19222222222-2-222-2-2222222222-2-20000-2-22222-2-2-2000000-200000000000000002222000000000000000000-2-20000
χ20222222222-2-222-2-2222222222-2-20000-2-22222-2-2-2000000-20000000000000000-2-2-2-2000000000000000000220000
χ21222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-22000000200000000000000000000000000000000002-22-2000000
χ22222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2200000020000000000000000000000000000000000-22-22000000
χ2322222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-2-22222-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1111111111111111100000000000022-1-1-1-10000000000
χ2722222222-122-2-222-2-2-1-1-1-1-1-1-1-2-22222-1-11111-1-11-2-200001-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2822222222-122-2-222-2-2-1-1-1-1-1-1-1-2-22222-1-11111-1-11-2-200001-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2922222222-122-2-222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-11220000111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3022222222-122-2-222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-11220000111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-2-2-222222-2-2-2-22-22i2i−2i−2i22-2-222-2-22−2i2i0000-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ322222-2-2-2-2222-2-2-2-222222-2-2-2-22-2−2i−2i2i2i22-2-222-2-222i−2i0000-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ332222-2-2-2-22-2-22222-2-2222-2-2-2-22-20000-2-222-2-2222000000-200000000000000002i2i−2i−2i000000000000000000−2i2i0000
χ342222-2-2-2-22-2-22222-2-2222-2-2-2-22-20000-2-222-2-2222000000-20000000000000000−2i−2i2i2i0000000000000000002i−2i0000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-220000-2-2-2-22222-2000000200000000000000000000000000000000002-2-22000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-220000-2-2-2-22222-200000020000000000000000000000000000000000-222-2000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-222i2i−2i−2i-1-1-1-1111112i−2i2i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-1110000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-222i2i−2i−2i-1-1-1-1111112i−2i−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-10000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-22−2i−2i2i2i-1-1-1-111111−2i2i2i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-10000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-22−2i−2i2i2i-1-1-1-111111−2i2i−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-1110000000000
χ412222-2-2-2-2-122-2-2-2-222-1-1-111112-22i2i−2i−2i-1-111-1-111-1−2i2i00001−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i30000000000
χ422222-2-2-2-2-122-2-2-2-222-1-1-111112-22i2i−2i−2i-1-111-1-111-1−2i2i00001−i−iiiii−i−i−3−33333−3−300000000000000i3−i3−i3i30000000000
χ432222-2-2-2-2-122-2-2-2-222-1-1-111112-2−2i−2i2i2i-1-111-1-111-12i−2i00001ii−i−i−i−iii33−3−3−3−33300000000000000i3−i3−i3i30000000000
χ442222-2-2-2-2-122-2-2-2-222-1-1-111112-2−2i−2i2i2i-1-111-1-111-12i−2i00001ii−i−i−i−iii−3−33333−3−300000000000000−i3i3i3−i30000000000
χ4522-2-22i2i−2i−2i2002-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i000001+i−1−i1−i−1+i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322−2−2−i2−i2i2i20000000000000000
χ4622-2-22i2i−2i−2i2002-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i000001+i−1−i1−i−1+i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2−222i2i2−i2−i20000000000000000
χ4722-2-22i2i−2i−2i2002-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i00000−1−i1+i−1+i1−i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2−222i2i2−i2−i20000000000000000
χ4822-2-22i2i−2i−2i2002-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i00000−1−i1+i−1+i1−i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322−2−2−i2−i2i2i20000000000000000
χ4922-2-2−2i−2i2i2i2002-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i000001−i−1+i1+i−1−i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322−2−2i2i2−i2−i20000000000000000
χ5022-2-2−2i−2i2i2i2002-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i000001−i−1+i1+i−1−i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2−222−i2−i2i2i20000000000000000
χ5122-2-2−2i−2i2i2i2002-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i00000−1+i1−i−1−i1+i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2−222−i2−i2i2i20000000000000000
χ5222-2-2−2i−2i2i2i2002-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i00000−1+i1−i−1−i1+i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322−2−2i2i2−i2−i20000000000000000
χ532-22-22i−2i2i−2i22-2002i−2i00-22-22i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-200002i−2i000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000002−22−2−i2i2−i2i20000000000001+i−1−i1−i−1+i
χ542-22-22i−2i2i−2i22-2002i−2i00-22-22i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-200002i−2i000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000−22−22i2−i2i2−i2000000000000−1−i1+i−1+i1−i
χ552-22-22i−2i2i−2i22-2002i−2i00-22-22i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-200002i−2i00000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000002−22−2−i2i2−i2i2000000000000−1−i1+i−1+i1−i
χ562-22-22i−2i2i−2i22-2002i−2i00-22-22i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-200002i−2i00000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000−22−22i2−i2i2−i20000000000001+i−1−i1−i−1+i
χ572-22-2−2i2i−2i2i22-200−2i2i00-22-2−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-20000−2i2i00000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000002−22−2i2−i2i2−i20000000000001−i−1+i1+i−1−i
χ582-22-2−2i2i−2i2i22-200−2i2i00-22-2−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-20000−2i2i00000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000−22−22−i2i2−i2i2000000000000−1+i1−i−1−i1+i
χ592-22-2−2i2i−2i2i22-200−2i2i00-22-2−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-20000−2i2i000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000002−22−2i2−i2i2−i2000000000000−1+i1−i−1−i1+i
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χ824-44-4−4i4i−4i4i-24-400−4i4i002-222i−2i2i−2i004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-2200002i−2i00000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i-2-44004i−4i002-222i−2i2i−2i0000002-20000−2i2i0000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i-2-44004i−4i002-222i−2i2i−2i0000002-20000−2i2i00000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ854-4-444-4-44400000000-4-444-4-440000000000000000000000000000000000000000002-2-222-2-220000000000000000
χ864-4-444-4-44400000000-4-444-4-44000000000000000000000000000000000000000000-222-2-222-20000000000000000
χ874-4-44-444-4400000000-4-44-444-40000000000000000000000000000000000000000002-2-22-222-20000000000000000
χ884-4-44-444-4400000000-4-44-444-4000000000000000000000000000000000000000000-222-22-2-220000000000000000
χ898-8-888-8-88-40000000044-4-444-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-888-8-40000000044-44-4-44000000000000000000000000000000000000000000000000000000000000000000

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