Finite Group Databasebeta

← Group #10713688

Character table — Group #10713688

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222222244444444444444444444444444444444888888888888888888888888242424242424242448484848
order1222223444466688888888121212122424242424242424444466888812121212121212121212242424242424242424242424161616161616161648484848484848484848484848484848444488882244
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
χ51111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91-1-11-111-111-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101-1-11-111-111-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111-1-11-111-111-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121-1-11-111-111-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131-1-11-111-111-1-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141-1-11-111-111-1-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151-1-11-111-111-1-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161-1-11-111-111-1-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-22222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222-2-2-2-2-2-2-2-22-2-2-2-222222222000000000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ19222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ21222222-12222-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-111111111-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ22222222-12222-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-111111111-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ23222222-12222-1-1-1-2-22222-2-2-1-1-1-111111111-2-2-2-2-1-1-2-222-111111111-11111-1-1-1-1-1-1-1-10000000033−3−333−3−333−3−333−3−3000000000000
χ24222222-12222-1-1-1-2-22222-2-2-1-1-1-111111111-2-2-2-2-1-1-2-222-111111111-11111-1-1-1-1-1-1-1-100000000−3−333−3−333−3−333−3−333000000000000
χ25222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111110000000033−3−333−3−3−3−333−3−333000000000000
χ26222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000−3−333−3−33333−3−333−3−3000000000000
χ272222-2-2222-2-2222220000222222222222220000-2-2-2-200-200000000-2-2-2-2-2000000000000000000000000000000002-22-200000000
χ282222-2-2222-2-2222220000222222222222220000-2-2-2-200-200000000-2-2-2-2-200000000000000000000000000000000-22-2200000000
χ292222-2-2222-2-2222-2-20000-2-22222-2-2-2-2-2-2-2-20000-2-22200-200000000-222220000000000000000000000000000000000002i−2i2i−2i0000
χ302222-2-2222-2-2222-2-20000-2-22222-2-2-2-2-2-2-2-20000-2-22200-200000000-22222000000000000000000000000000000000000−2i2i−2i2i0000
χ312222-2-22-2-22222200222200-2-2-2-2000000000000-2-200-2-22000000002000022-2-222-2-22−22−22−22−22−22−22−22−22−22−22−22−2000000000000
χ322222-2-22-2-22222200222200-2-2-2-2000000000000-2-200-2-22000000002000022-2-222-2-2−22−22−22−22−22−22−22−22−22−22−22−22000000000000
χ332222-2-22-2-22222200-2-2-2-200-2-2-2-2000000000000-2-2002220000000020000-2-222-2-2222−22−2−22−222−22−22−22−2−22−22−22−22000000000000
χ342222-2-22-2-22222200-2-2-2-200-2-2-2-2000000000000-2-2002220000000020000-2-222-2-222−22−222−22−2−22−22−22−222−22−22−22−2000000000000
χ352222-2-2-1-2-222-1-1-100222200111133−3−333−3−300001100-2-2-133−3−333−3−3-13−33−3-1-111-1-1112−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ362222-2-2-1-2-222-1-1-100222200111133−3−333−3−300001100-2-2-133−3−333−3−3-13−33−3-1-111-1-111−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ372222-2-2-1-2-222-1-1-1002222001111−3−333−3−33300001100-2-2-1−3−333−3−333-1−33−33-1-111-1-1112−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ382222-2-2-1-2-222-1-1-1002222001111−3−333−3−33300001100-2-2-1−3−333−3−333-1−33−33-1-111-1-111−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ392222-2-2-1-2-222-1-1-100-2-2-2-200111133−3−333−3−30000110022-1−3−333−3−333-13−33−311-1-111-1-12−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ402222-2-2-1-2-222-1-1-100-2-2-2-200111133−3−333−3−30000110022-1−3−333−3−333-13−33−311-1-111-1-1−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ412222-2-2-1-2-222-1-1-100-2-2-2-2001111−3−333−3−3330000110022-133−3−333−3−3-1−33−3311-1-111-1-12−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ422222-2-2-1-2-222-1-1-100-2-2-2-2001111−3−333−3−3330000110022-133−3−333−3−3-1−33−3311-1-111-1-1−22−222−22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ432-2-222-222-22-2-2-220022-2-20022-2-20000000000002-200-22-2000000002000022-2-2-2-222−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-2-222-222-22-2-2-220022-2-20022-2-20000000000002-200-22-2000000002000022-2-2-2-222i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-222-222-22-2-2-2200-2-2220022-2-20000000000002-2002-2-20000000020000-2-22222-2-2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ462-2-222-222-22-2-2-2200-2-2220022-2-20000000000002-2002-2-20000000020000-2-22222-2-2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ472-2-222-22-22-22-2-22220000-2-2-2-2222222-2-2-2-200002-2-2200200000000-2-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ482-2-222-22-22-22-2-22220000-2-2-2-2222222-2-2-2-200002-2-2200200000000-2-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ492-2-222-22-22-22-2-22-2-2000022-2-222-2-2-2-2222200002-22-200200000000-222-2-20000000000000000000000000000000000002-2-220000
χ502-2-222-22-22-22-2-22-2-2000022-2-222-2-2-2-2222200002-22-200200000000-222-2-2000000000000000000000000000000000000-222-20000
χ512-2-222-2-12-22-211-10022-2-200-1-11133−3−3−3−3330000-1100-22133−3−3−3−333-13−3−33-1-11111-1-1−i2i2i2−i2−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ522-2-222-2-12-22-211-10022-2-200-1-11133−3−3−3−3330000-1100-22133−3−3−3−333-13−3−33-1-11111-1-1i2−i2−i2i2i2−i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ532-2-222-2-12-22-211-10022-2-200-1-111−3−33333−3−30000-1100-221−3−33333−3−3-1−333−3-1-11111-1-1−i2i2i2−i2−i2i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ542-2-222-2-12-22-211-10022-2-200-1-111−3−33333−3−30000-1100-221−3−33333−3−3-1−333−3-1-11111-1-1i2−i2−i2i2i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ552-2-222-2-12-22-211-100-2-22200-1-11133−3−3−3−3330000-11002-21−3−33333−3−3-13−3−3311-1-1-1-111−i2i2i2−i2i2−i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ562-2-222-2-12-22-211-100-2-22200-1-11133−3−3−3−3330000-11002-21−3−33333−3−3-13−3−3311-1-1-1-111i2−i2−i2i2−i2i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ572-2-222-2-12-22-211-100-2-22200-1-111−3−33333−3−30000-11002-2133−3−3−3−333-1−333−311-1-1-1-111−i2i2i2−i2i2−i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ582-2-222-2-12-22-211-100-2-22200-1-111−3−33333−3−30000-11002-2133−3−3−3−333-1−333−311-1-1-1-111i2−i2−i2i2−i2i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ592-2-22-222-222-2-2-22-2-222-2-222-2-222-2-2-2-22222-2-222-22-222-2-2-2-2-2-222222-2-2222222-2-2-2-2000000000000000000000000000000000000
χ602-2-22-222-222-2-2-22-2-2-2-22222-2-222-2-2-2-2222222-2-2-22-22-22-22222-2-2-2-22-2-222-2-2-2-22222000000000000000000000000000000000000
χ612-2-22-22-1-222-211-12222-2-2-2-211-1-1-1-1-1-1111122-2-21-12-22-21-1-1-1-11111-1-1-111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000
χ622-2-22-22-1-222-211-12222-2-2-2-211-1-1-1-1-1-1111122-2-21-12-22-21-1-1-1-11111-1-1-111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000
χ632-2-22-22-1-222-211-122-2-222-2-211-1-1-1-1-1-11111-2-2221-12-2-2211111-1-1-1-1-1-1-1111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ642-2-22-22-1-222-211-122-2-222-2-211-1-1-1-1-1-11111-2-2221-12-2-2211111-1-1-1-1-1-1-1111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000
χ652-2-22-22-1-222-211-1-2-222-2-22211-1-11111-1-1-1-1-2-2221-1-222-211111-1-1-1-1-111-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ662-2-22-22-1-222-211-1-2-222-2-22211-1-11111-1-1-1-1-2-2221-1-222-211111-1-1-1-1-111-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ672-2-22-22-1-222-211-1-2-2-2-2222211-1-11111-1-1-1-122-2-21-1-22-221-1-1-1-11111-111-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ682-2-22-22-1-222-211-1-2-2-2-2222211-1-11111-1-1-1-122-2-21-1-22-221-1-1-1-11111-111-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ694444444-4-4-4-444400000000-4-4-4-4000000000000440000-400000000-4000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-20000000022222323−23−232323−23−230000-2-200002000000002−2323−232300000000000000000000000000000000000000000000
χ71444444-2-4-4-4-4-2-2-2000000002222−23−232323−23−2323230000-2-20000200000000223−2323−2300000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.