Finite Group Databasebeta

← Group #10695161

Character table — Group #10695161

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12224444223444444444466612121212668888888812121212121212121212242424242424242424242424242424248888888888888888448812121212242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ1722222222222-2-2-2-2-2-2-2-2222222222220000000022-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222222222220000000022-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ2322222222-2-2222-2-222-2-2-2-22222222-2-222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2222-2-222-2-2-2-22222222-2-2-2-222-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-22-2-222-2-222-2-22222222-2-200000000-2-2-2-22222-2-200000000000000000000000022-2-222-2-20000000000000000
χ2622222222-2-22-2-222-2-222-2-22222222-2-200000000-2-2-2-22222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2722222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-11122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-11122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-111-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-111-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2-2-222222-2-2-2-222-2-2222-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ322222-2-2-2-222222-2-2-2-222-2-2222-2-2-2-222−2i−2i2i2i2i2i−2i−2i-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ332222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ342222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ352222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-12i2i−2i−2i−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−i3i3i3−i33−3−330000
χ362222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-12i2i−2i−2i−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000i3−i3−i3i3−333−30000
χ372222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-1−2i−2i2i2i2i2i−2i−2i11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−i3i3i3−i3−333−30000
χ382222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-1−2i−2i2i2i2i2i−2i−2i11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000i3−i3−i3i33−3−330000
χ392222-2-2-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-20000000022-2-2-2-22222000000000000000022-2-2-2-222000000000000000000000000
χ402222-2-2-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-20000000022-2-2-2-222220000000000000000-2-22222-2-2000000000000000000000000
χ412222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i-1-111−i−iii0000
χ422222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ432222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ442222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ452-2-2222-2-22-22000000002-22-2-2-2-2222-2−i2i2−i2i2−i2i2−i2i22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i2−22−22−22−20000000000000000
χ462-2-2222-2-22-22000000002-22-2-2-2-2222-2−i2i2−i2i2−i2i2−i2i22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i−22−22−22−220000000000000000
χ472-2-2222-2-22-22000000002-22-2-2-2-2222-2i2−i2i2−i2i2−i2i2−i22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i−22−22−22−220000000000000000
χ482-2-2222-2-22-22000000002-22-2-2-2-2222-2i2−i2i2−i2i2−i2i2−i22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i2−22−22−22−20000000000000000
χ492-2-2222-2-2-22200000000-222-2-2-2-222-22−i2i2i2−i2−i2i2i2−i2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22i−2i002i−2i002−2−222−2−220000000000000000
χ502-2-2222-2-2-22200000000-222-2-2-2-222-22−i2i2i2−i2−i2i2i2−i2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−2i2i00−2i2i00−222−2−222−20000000000000000
χ512-2-2222-2-2-22200000000-222-2-2-2-222-22i2−i2−i2i2i2−i2−i2i2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22i−2i002i−2i00−222−2−222−20000000000000000
χ522-2-2222-2-2-22200000000-222-2-2-2-222-22i2−i2−i2i2i2−i2−i2i2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−2i2i00−2i2i002−2−222−2−220000000000000000
χ532-2-22-2-2222-2200000000-222-2-222-2-22-22−2−22−222−2-220000000022−2−2−2−222−2−22222−2−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ542-2-22-2-2222-2200000000-222-2-222-2-22-22−2−22−222−2-220000000022−2−2−2−222−2−22222−2−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ552-2-22-2-2222-2200000000-222-2-222-2-22-2−222−22−2−22-2200000000−2−22222−2−222−2−2−2−2222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ562-2-22-2-2222-2200000000-222-2-222-2-22-2−222−22−2−22-2200000000−2−22222−2−222−2−2−2−222−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ572-2-22-2-222-222000000002-22-2-222-2-2-222−22−2−22−222-20000000022−2−222−2−2−2−222−2−222002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ582-2-22-2-222-222000000002-22-2-222-2-2-222−22−2−22−222-20000000022−2−222−2−2−2−222−2−22200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ592-2-22-2-222-222000000002-22-2-222-2-2-22−22−222−22−22-200000000−2−222−2−22222−2−222−2−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ602-2-22-2-222-222000000002-22-2-222-2-2-22−22−222−22−22-200000000−2−222−2−22222−2−222−2−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ614444444444-2-4-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-200000000-2-222222222000000000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-444-4-444-4-4-2-2-2-2-2-2-222000000002222-2-2-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-2-4-44444-4-4-4-4-2-2-22222-2-2000000002222-2-222-2-2000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-2-4-4-4-4444444-2-2-222222200000000-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
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χ774-44-44i−4i−4i4i0044-4004i−4i0000-4-44−4i4i4i−4i0000000000004-400004i−4i000000000000000000000000000000000000000000000000
χ784-44-44i−4i−4i4i004-4400−4i4i0000-4-44−4i4i4i−4i000000000000-440000−4i4i000000000000000000000000000000000000000000000000
χ794-44-44i−4i−4i4i00-24-4004i−4i000022-22i−2i−2i2i000000000000-220000−2i2i00002ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ130000−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000
χ804-44-44i−4i−4i4i00-24-4004i−4i000022-22i−2i−2i2i000000000000-220000−2i2i0000−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ1300002ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000
χ814-44-44i−4i−4i4i00-2-4400−4i4i000022-22i−2i−2i2i0000000000002-200002i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ130000−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000000000
χ824-44-44i−4i−4i4i00-2-4400−4i4i000022-22i−2i−2i2i0000000000002-200002i−2i−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ1300002ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000000000
χ834-44-4−4i4i4i−4i0044-400−4i4i0000-4-444i−4i−4i4i0000000000004-40000−4i4i000000000000000000000000000000000000000000000000
χ844-44-4−4i4i4i−4i004-44004i−4i0000-4-444i−4i−4i4i000000000000-4400004i−4i000000000000000000000000000000000000000000000000
χ854-44-4−4i4i4i−4i00-24-400−4i4i000022-2−2i2i2i−2i000000000000-2200002i−2i0000−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ2300002ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000
χ864-44-4−4i4i4i−4i00-24-400−4i4i000022-2−2i2i2i−2i000000000000-2200002i−2i00002ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ230000−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000
χ874-44-4−4i4i4i−4i00-2-44004i−4i000022-2−2i2i2i−2i0000000000002-20000−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ2300002ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ884-44-4−4i4i4i−4i00-2-44004i−4i000022-2−2i2i2i−2i0000000000002-20000−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ230000−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ894-4-4444-4-44-4-2000000004-4-22222-2-2-22−2i22i2−2i22i2−2i22i2−2i22i2-2200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ904-4-4444-4-44-4-2000000004-4-22222-2-2-222i2−2i22i2−2i22i2−2i22i2−2i2-2200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ914-4-4444-4-4-44-200000000-44-22222-2-22-2−2i22i22i2−2i2−2i22i22i2−2i22-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ924-4-4444-4-4-44-200000000-44-22222-2-22-22i2−2i2−2i22i22i2−2i2−2i22i22-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ934-4-44-4-4444-4-200000000-44-222-2-222-2222−22−2222−222222−222-200000000−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ944-4-44-4-4444-4-200000000-44-222-2-222-22−222222−2222−22−22222-20000000022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ954-4-44-4-444-44-2000000004-4-222-2-2222-222−2222−22−2222−2222-2200000000−2−222−2−22222−2−222−2−200000000000000000000000000000000
χ964-4-44-4-444-44-2000000004-4-222-2-2222-2−2222−222222−2222−22-220000000022−2−222−2−2−2−222−2−22200000000000000000000000000000000

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