Finite Group Databasebeta

← Group #10694553

Character table — Group #10694553

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12224444223444444666121212121212121212121212446688888888121212121212242424242424242424242424242424248888888824242424242424242424242424242424444488882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-111111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222-2-222-2-2222-2-2-2-22222-2-2-2-2-2-22222-2-222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222-2-222-2-2222-2-2-2-22222-2-2-2-2-2-222-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ202222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ212222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ232222222222-1-2-222-2-2-1-1-11111-1-1-1-11111-2-2-1-122-2-222-2-21111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−3000000000000
χ242222222222-1-2-222-2-2-1-1-11111-1-1-1-11111-2-2-1-122-2-222-2-21111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−333000000000000
χ252222222222-1-2-222-2-2-1-1-11111-1-1-1-11111-2-2-1-1-2-222-2-2221111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−333000000000000
χ262222222222-1-2-222-2-2-1-1-11111-1-1-1-11111-2-2-1-1-2-222-2-2221111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−3000000000000
χ2722222222-2-2222-2-222222222222222222-2-2-2-200000000-2-2-2-2-2-2000000000000000000000000000000000000000000002-22-20000
χ2822222222-2-2222-2-222222222222222222-2-2-2-200000000-2-2-2-2-2-200000000000000000000000000000000000000000000-22-220000
χ2922222222-2-22-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222-2-2000000002222-2-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ3022222222-2-22-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222-2-2000000002222-2-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ312222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-2-222200000000-2-222-2-2000000000000000000000000000000000000000000002i−2i−2i2i0000
χ322222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-2-222200000000-2-222-2-200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-222222-2220000000022-2-2-2-200000000000000000000000000000000000000002-2-2200000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-222222-2220000000022-2-2-2-20000000000000000000000000000000000000000-222-200000000
χ352222-2-2-2-2-2-22-2-22222222-2-2-2-2-2-2-2-22222-22-2-222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-22222222-2-2-2-2-2-2-2-22222-22-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-1111111112-2112222-2-2-2-2-1-111-1-1-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000
χ382222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-1111111112-2112222-2-2-2-2-1-111-1-1-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000
χ392222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-1111111112-211-2-2-2-22222-1-111-1-111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ402222-2-2-2-2-2-2-12222-2-2-1-1-1-1-1-1-1111111112-211-2-2-2-22222-1-111-1-111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000
χ412222-2-2-2-2-2-2-1-2-22222-1-1-111111111-1-1-1-1-221122-2-2-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ422222-2-2-2-2-2-2-1-2-22222-1-1-111111111-1-1-1-1-221122-2-2-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ432222-2-2-2-2-2-2-1-2-22222-1-1-111111111-1-1-1-1-2211-2-22222-2-211-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ442222-2-2-2-2-2-2-1-2-22222-1-1-111111111-1-1-1-1-2211-2-22222-2-211-1-1-1-11111-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ4522-2-222-2-2-222002-2002-2-2000022-2-20000002-2002i−2i002i−2i00002-200002i2i−2i−2i00002i2i−2i−2i2−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ4622-2-222-2-2-222002-2002-2-2000022-2-20000002-2002i−2i002i−2i00002-200002i2i−2i−2i00002i2i−2i−2i−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ4722-2-222-2-2-222002-2002-2-2000022-2-20000002-200−2i2i00−2i2i00002-20000−2i−2i2i2i0000−2i−2i2i2i2−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ4822-2-222-2-2-222002-2002-2-2000022-2-20000002-200−2i2i00−2i2i00002-20000−2i−2i2i2i0000−2i−2i2i2i−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ4922-2-222-2-2-22-1002-200-11133−3−3-1-11133−3−300-11002i−2i002i−2i3−33−3-11−i3−i3i3i3−i−iii−i3−i3i3i3−i−iii2−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5022-2-222-2-2-22-1002-200-11133−3−3-1-11133−3−300-11002i−2i002i−2i3−33−3-11−i3−i3i3i3−i−iii−i3−i3i3i3−i−iii−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5122-2-222-2-2-22-1002-200-11133−3−3-1-11133−3−300-1100−2i2i00−2i2i3−33−3-11i3i3−i3−i3ii−i−ii3i3−i3−i3ii−i−i2−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5222-2-222-2-2-22-1002-200-11133−3−3-1-11133−3−300-1100−2i2i00−2i2i3−33−3-11i3i3−i3−i3ii−i−ii3i3−i3−i3ii−i−i−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5322-2-222-2-2-22-1002-200-111−3−333-1-111−3−33300-11002i−2i002i−2i−33−33-11i3i3−i3−i3−i−iiii3i3−i3−i3−i−iii2−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5422-2-222-2-2-22-1002-200-111−3−333-1-111−3−33300-11002i−2i002i−2i−33−33-11i3i3−i3−i3−i−iiii3i3−i3−i3−i−iii−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5522-2-222-2-2-22-1002-200-111−3−333-1-111−3−33300-1100−2i2i00−2i2i−33−33-11−i3−i3i3i3ii−i−i−i3−i3i3i3ii−i−i2−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5622-2-222-2-2-22-1002-200-111−3−333-1-111−3−33300-1100−2i2i00−2i2i−33−33-11−i3−i3i3i3ii−i−i−i3−i3i3i3ii−i−i−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5722-2-2-2-2222-22002-2002-2-20000-2-222000000-22002i−2i00−2i2i00002-200002i2i−2i−2i0000−2i−2i2i2i−i2i2i2−i2−222−2−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ5822-2-2-2-2222-22002-2002-2-20000-2-222000000-22002i−2i00−2i2i00002-200002i2i−2i−2i0000−2i−2i2i2ii2−i2−i2i22−2−22i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ5922-2-2-2-2222-22002-2002-2-20000-2-222000000-2200−2i2i002i−2i00002-20000−2i−2i2i2i00002i2i−2i−2i−i2i2i2−i22−2−22−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ6022-2-2-2-2222-22002-2002-2-20000-2-222000000-2200−2i2i002i−2i00002-20000−2i−2i2i2i00002i2i−2i−2ii2−i2−i2i2−222−2i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ6122-2-2-2-2222-2-1002-200-11133−3−311-1-1−3−333001-1002i−2i00−2i2i3−3−33-11−i3−i3i3i3−i−iiii3i3−i3−i3ii−i−i−i2i2i2−i2−222−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ6222-2-2-2-2222-2-1002-200-11133−3−311-1-1−3−333001-1002i−2i00−2i2i3−3−33-11−i3−i3i3i3−i−iiii3i3−i3−i3ii−i−ii2−i2−i2i22−2−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ6322-2-2-2-2222-2-1002-200-11133−3−311-1-1−3−333001-100−2i2i002i−2i3−3−33-11i3i3−i3−i3ii−i−i−i3−i3i3i3−i−iii−i2i2i2−i22−2−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ6422-2-2-2-2222-2-1002-200-11133−3−311-1-1−3−333001-100−2i2i002i−2i3−3−33-11i3i3−i3−i3ii−i−i−i3−i3i3i3−i−iiii2−i2−i2i2−222−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ6522-2-2-2-2222-2-1002-200-111−3−33311-1-133−3−3001-1002i−2i00−2i2i−333−3-11i3i3−i3−i3−i−iii−i3−i3i3i3ii−i−i−i2i2i2−i2−222−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ6622-2-2-2-2222-2-1002-200-111−3−33311-1-133−3−3001-1002i−2i00−2i2i−333−3-11i3i3−i3−i3−i−iii−i3−i3i3i3ii−i−ii2−i2−i2i22−2−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ6722-2-2-2-2222-2-1002-200-111−3−33311-1-133−3−3001-100−2i2i002i−2i−333−3-11−i3−i3i3i3ii−i−ii3i3−i3−i3−i−iii−i2i2i2−i22−2−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
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χ1014-4-44−4i4i4i−4i00-2-44004i−4i22-22-2-222i−2i−2i2i2i−2i−2i2i000000000000000000i6−i6−i6i6−i6i6i6−i6−666−6−666−6000000000000000000000000000000000000
χ1024-4-44−4i4i4i−4i00-2-44004i−4i22-22-2-222i−2i−2i2i2i−2i−2i2i000000000000000000−i6i6i6−i6i6−i6−i6i66−6−666−6−66000000000000000000000000000000000000

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