Finite Group Databasebeta

← Group #10694548

Character table — Group #10694548

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12224444223444444666121212121212121212121212446688888888121212121212242424242424242424242424242424248888888824242424242424242424242424242424444488882244
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
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−i11-1-1
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-1-111
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-1-111
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−iii11-1-1
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
χ452-2-2222-2-22-22002-2002-2-2000022-2-20000002-2002-2002-200002-2000022-2-2000022-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ462-2-2222-2-22-22002-2002-2-2000022-2-20000002-2002-2002-200002-2000022-2-2000022-2-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ472-2-2222-2-22-22002-2002-2-2000022-2-20000002-200-2200-2200002-20000-2-2220000-2-222−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ482-2-2222-2-22-22002-2002-2-2000022-2-20000002-200-2200-2200002-20000-2-2220000-2-222i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ492-2-2222-2-22-2-1002-200-11133−3−3-1-11133−3−300-11002-2002-23−33−3-1133−3−3-1-11133−3−3-1-111−i2i2−i2i2−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ502-2-2222-2-22-2-1002-200-11133−3−3-1-11133−3−300-11002-2002-23−33−3-1133−3−3-1-11133−3−3-1-111i2−i2i2−i2i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ512-2-2222-2-22-2-1002-200-11133−3−3-1-11133−3−300-1100-2200-223−33−3-11−3−33311-1-1−3−33311-1-1−i2i2−i2i2i2−i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ522-2-2222-2-22-2-1002-200-11133−3−3-1-11133−3−300-1100-2200-223−33−3-11−3−33311-1-1−3−33311-1-1i2−i2i2−i2−i2i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ532-2-2222-2-22-2-1002-200-111−3−333-1-111−3−33300-11002-2002-2−33−33-11−3−333-1-111−3−333-1-111−i2i2−i2i2−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ542-2-2222-2-22-2-1002-200-111−3−333-1-111−3−33300-11002-2002-2−33−33-11−3−333-1-111−3−333-1-111i2−i2i2−i2i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ552-2-2222-2-22-2-1002-200-111−3−333-1-111−3−33300-1100-2200-22−33−33-1133−3−311-1-133−3−311-1-1−i2i2−i2i2i2−i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ562-2-2222-2-22-2-1002-200-111−3−333-1-111−3−33300-1100-2200-22−33−33-1133−3−311-1-133−3−311-1-1i2−i2i2−i2−i2i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ572-2-22-2-222-222002-2002-2-20000-2-222000000-22002-200-2200002-2000022-2-20000-2-2222−2−222−2−222−22−2−22−222−22−2−22−22000000000000
χ582-2-22-2-222-222002-2002-2-20000-2-222000000-22002-200-2200002-2000022-2-20000-2-222−222−2−222−2−22−222−22−2−22−222−22−2000000000000
χ592-2-22-2-222-222002-2002-2-20000-2-222000000-2200-22002-200002-20000-2-222000022-2-22−2−22−222−22−22−2−22−22−22−222−22−2000000000000
χ602-2-22-2-222-222002-2002-2-20000-2-222000000-2200-22002-200002-20000-2-222000022-2-2−222−22−2−22−22−222−22−22−22−2−22−22000000000000
χ612-2-22-2-222-22-1002-200-11133−3−311-1-1−3−333001-1002-200-223−3−33-1133−3−3-1-111−3−33311-1-12−2−222−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ622-2-22-2-222-22-1002-200-11133−3−311-1-1−3−333001-1002-200-223−3−33-1133−3−3-1-111−3−33311-1-1−222−2−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ632-2-22-2-222-22-1002-200-11133−3−311-1-1−3−333001-100-22002-23−3−33-11−3−33311-1-133−3−3-1-1112−2−22−222−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ642-2-22-2-222-22-1002-200-11133−3−311-1-1−3−333001-100-22002-23−3−33-11−3−33311-1-133−3−3-1-111−222−22−2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ652-2-22-2-222-22-1002-200-111−3−33311-1-133−3−3001-1002-200-22−333−3-11−3−333-1-11133−3−311-1-12−2−222−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ662-2-22-2-222-22-1002-200-111−3−33311-1-133−3−3001-1002-200-22−333−3-11−3−333-1-11133−3−311-1-1−222−2−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ672-2-22-2-222-22-1002-200-111−3−33311-1-133−3−3001-100-22002-2−333−3-1133−3−311-1-1−3−333-1-1112−2−22−222−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ682-2-22-2-222-22-1002-200-111−3−33311-1-133−3−3001-100-22002-2−333−3-1133−3−311-1-1−3−333-1-111−222−22−2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ6944444444-4-4-244-4-444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-422000000002222220000000000000000000000000000000000000000000000000000
χ7044444444-4-4-2-4-4-4-4-4-4-2-2-22222-2-2-2-22222442200000000-2-2-2-2220000000000000000000000000000000000000000000000000000
χ714444-4-4-4-444-244-4-4-4-4-2-2-2-2-2-2-222222222-44-2-20000000022-2-2220000000000000000000000000000000000000000000000000000
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χ1004-4-44-4-4444-4400-44004-4-40000-4-4440000004-4000000000000-440000000000000000000000000000000000000000000000000000
χ1014-4-44-4-4444-4-200-4400-2222323−23−2322-2-2−23−23232300-2200000000−232323−232-20000000000000000000000000000000000000000000000000000
χ1024-4-44-4-4444-4-200-4400-222−23−23232322-2-22323−23−2300-220000000023−23−23232-20000000000000000000000000000000000000000000000000000

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