Finite Group Databasebeta

← Group #10690199

Character table — Group #10690199

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order12222222222236666666444444446666121212121212121244888888881212121212121212242424242424242424242424242424242222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ121111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111
χ131111-1-1-1-11-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii-1-111
χ141111-1-1-1-11-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i11-1-1
χ151111-1-1-1-11-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i-1-111
χ161111-1-1-1-11-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii11-1-1
χ1722222222222222222222-2-22222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222000000002222-2-2-2-200000000000000000000000000000000
χ19222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ21222222222222-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-111111111-2-2000000001111-1-1-1-133−3−333−3−333−3−333−3−30000000000000000
χ24222222222222-1-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-111111111-2-2000000001111-1-1-1-1−3−333−3−333−3−333−3−3330000000000000000
χ25222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112200000000-1-1-1-1111133−3−333−3−3−3−333−3−3330000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112200000000-1-1-1-11111−3−333−3−33333−3−333−3−30000000000000000
χ2722222222-2-2-2-2222222222-200002-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000002-22-200000000
χ2822222222-2-2-2-2222222222-200002-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000-22-2200000000
χ2922222222-2-2-2-222222222-220000-22-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-222222222-220000-22-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000-22-220000
χ312222-2-2-2-22-2-2222-2-2-2-222-2-222-2-22222-2-2-2-2-2-22222-2200000000-2-22222-2-200000000000000000000000000000000
χ322222-2-2-2-22-2-2222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-222222-20000000022-2-2-2-22200000000000000000000000000000000
χ332222-2-2-2-22-2-22-1-11111-1-12222-2-2-2-2-1-111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ342222-2-2-2-22-2-22-1-11111-1-12222-2-2-2-2-1-111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ352222-2-2-2-22-2-22-1-11111-1-122-2-222-2-2-1-111-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ362222-2-2-2-22-2-22-1-11111-1-122-2-222-2-2-1-111-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ372222-2-2-2-22-2-22-1-11111-1-1-2-222-2-222-1-1111111-1-1-1-1-220000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ382222-2-2-2-22-2-22-1-11111-1-1-2-222-2-222-1-1111111-1-1-1-1-220000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ392222-2-2-2-22-2-22-1-11111-1-1-2-2-2-22222-1-1111111-1-1-1-12-200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ402222-2-2-2-22-2-22-1-11111-1-1-2-2-2-22222-1-1111111-1-1-1-12-200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ412222-2-2-2-2-222-222-2-2-2-2222-20000-22-2-22222-2-2-2-222000000000000000000000000000000000000002i−2i−2i2i00000000
χ422222-2-2-2-2-222-222-2-2-2-2222-20000-22-2-22222-2-2-2-22200000000000000000000000000000000000000−2i2i2i−2i00000000
χ432222-2-2-2-2-222-222-2-2-2-222-2200002-2-2-222-2-22222-2-20000000000000000000000000000000000000000002i−2i−2i2i0000
χ442222-2-2-2-2-222-222-2-2-2-222-2200002-2-2-222-2-22222-2-2000000000000000000000000000000000000000000−2i2i2i−2i0000
χ452-22-222-2-222-2-22-222-2-22-2002i−2i2i−2i002-22-200000000002−22−2−i2i2−i2i200002i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ462-22-222-2-222-2-22-222-2-22-2002i−2i2i−2i002-22-20000000000−22−22i2−i2i2−i200002i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ472-22-222-2-222-2-22-222-2-22-200−2i2i−2i2i002-22-200000000002−22−2i2−i2i2−i20000−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ482-22-222-2-222-2-22-222-2-22-200−2i2i−2i2i002-22-20000000000−22−22−i2i2−i2i20000−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ492-22-222-2-222-2-2-11-1-111-11002i−2i2i−2i00-11-113−33−33−33−3002−22−2−i2i2−i2i2−i3i3−i3i3−ii−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ502-22-222-2-222-2-2-11-1-111-11002i−2i2i−2i00-11-113−33−33−33−300−22−22i2−i2i2−i2−i3i3−i3i3−ii−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ512-22-222-2-222-2-2-11-1-111-11002i−2i2i−2i00-11-11−33−33−33−33002−22−2−i2i2−i2i2i3−i3i3−i3−ii−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ522-22-222-2-222-2-2-11-1-111-11002i−2i2i−2i00-11-11−33−33−33−3300−22−22i2−i2i2−i2i3−i3i3−i3−ii−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ532-22-222-2-222-2-2-11-1-111-1100−2i2i−2i2i00-11-113−33−33−33−3002−22−2i2−i2i2−i2i3−i3i3−i3i−ii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ542-22-222-2-222-2-2-11-1-111-1100−2i2i−2i2i00-11-113−33−33−33−300−22−22−i2i2−i2i2i3−i3i3−i3i−ii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ552-22-222-2-222-2-2-11-1-111-1100−2i2i−2i2i00-11-11−33−33−33−33002−22−2i2−i2i2−i2−i3i3−i3i3i−ii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ562-22-222-2-222-2-2-11-1-111-1100−2i2i−2i2i00-11-11−33−33−33−3300−22−22−i2i2−i2i2−i3i3−i3i3i−ii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ572-22-2-2-2222-22-22-2-2-2222-2002i−2i−2i2i002-2-220000000000−i2i2i2−i2−222−200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ582-22-2-2-2222-22-22-2-2-2222-2002i−2i−2i2i002-2-220000000000i2−i2−i2i22−2−2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ592-22-2-2-2222-22-22-2-2-2222-200−2i2i2i−2i002-2-220000000000−i2i2i2−i22−2−220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ602-22-2-2-2222-22-22-2-2-2222-200−2i2i2i−2i002-2-220000000000i2−i2−i2i2−222−20000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ612-22-2-2-2222-22-2-1111-1-1-11002i−2i−2i2i00-111-13−33−3−33−3300−i2i2i2−i2−222−2−i3i3i3−i3−iii−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ622-22-2-2-2222-22-2-1111-1-1-11002i−2i−2i2i00-111-13−33−3−33−3300i2−i2−i2i22−2−22−i3i3i3−i3−iii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ632-22-2-2-2222-22-2-1111-1-1-11002i−2i−2i2i00-111-1−33−333−33−300−i2i2i2−i2−222−2i3−i3−i3i3−iii−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ642-22-2-2-2222-22-2-1111-1-1-11002i−2i−2i2i00-111-1−33−333−33−300i2−i2−i2i22−2−22i3−i3−i3i3−iii−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ652-22-2-2-2222-22-2-1111-1-1-1100−2i2i2i−2i00-111-13−33−3−33−3300−i2i2i2−i22−2−22i3−i3−i3i3i−i−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ662-22-2-2-2222-22-2-1111-1-1-1100−2i2i2i−2i00-111-13−33−3−33−3300i2−i2−i2i2−222−2i3−i3−i3i3i−i−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ672-22-2-2-2222-22-2-1111-1-1-1100−2i2i2i−2i00-111-1−33−333−33−300−i2i2i2−i22−2−22−i3i3i3−i3i−i−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ682-22-2-2-2222-22-2-1111-1-1-1100−2i2i2i−2i00-111-1−33−333−33−300i2−i2−i2i2−222−2−i3i3i3−i3i−i−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ6944444444-4-4-4-4-2-2-2-2-2-2-2-24-400004-42222-2-222-2-22200000000000000000000000000000000000000000000000000
χ7044444444-4-4-4-4-2-2-2-2-2-2-2-2-440000-44222222-2-222-2-200000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-444-4-2-22222-2-24-40000-4422-2-2-2-22222-2-200000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-444-4-2-22222-2-2-4400004-422-2-222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7344-4-44-44-40000444-44-4-4-40000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ7444-4-44-44-40000444-44-4-4-4000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ7544-4-4-44-44000044-44-44-4-40000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ7644-4-4-44-44000044-44-44-4-4000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ774-44-444-4-4-4-4444-444-4-44-400000000-44-440000000000000000000000000000000000000000000000000000000000
χ784-44-444-4-4-4-444-22-2-222-22000000002-22-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ794-44-444-4-4-4-444-22-2-222-22000000002-22-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ804-44-4-4-444-44-444-4-4-4444-400000000-444-40000000000000000000000000000000000000000000000000000000000
χ814-44-4-4-444-44-44-2222-2-2-22000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ824-44-4-4-444-44-44-2222-2-2-22000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ834-4-444-4-4400004-44-4-44-440000000000000000000000000000000000000000000000000000002-22-2000000000000
χ844-4-444-4-4400004-44-4-44-44000000000000000000000000000000000000000000000000000000-22-22000000000000
χ854-4-44-444-400004-4-444-4-440000000000000000000000000000000000000000000000000000002-2-22000000000000
χ864-4-44-444-400004-4-444-4-44000000000000000000000000000000000000000000000000000000-222-2000000000000
χ8788-8-88-88-80000-4-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-880000-4-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-888-8-880000-44-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-888-80000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000

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