Finite Group Databasebeta

← Group #10713683

Character table — Group #10713683

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222222244444444444444444444444444444444888888888888888888888888242424242424242448484848
order1244222344466688888888121212122424242424242424444466888812121212121212121212242424242424242424242424161616161616161648484848484848484848484848484848444488882244
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
χ51111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ81111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911-1-1-11-11-111-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ1011-1-1-11-11-111-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ1111-1-1-11-11-111-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ1211-1-1-11-11-111-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ1311-1-1-11-11-111-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411-1-1-11-11-111-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511-1-1-11-11-111-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611-1-1-11-11-111-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-11-1-1-1-1-11111111-1-1-1-1-1-11111−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
χ192222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ202222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ212222222-1222-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-111111111-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ222222222-1222-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-111111111-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ232222222-1222-1-1-1-2-22222-2-2-1-1-1-111111111-2-2-2-2-1-1-2-222-111111111-11111-1-1-1-1-1-1-1-10000000033−3−333−3−333−3−333−3−3000000000000
χ242222222-1222-1-1-1-2-22222-2-2-1-1-1-111111111-2-2-2-2-1-1-2-222-111111111-11111-1-1-1-1-1-1-1-100000000−3−333−3−333−3−333−3−333000000000000
χ252222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111110000000033−3−333−3−3−3−333−3−333000000000000
χ262222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000−3−333−3−33333−3−333−3−3000000000000
χ2722222-2-22-22-2222220000222222222222220000-2-2-2-200-200000000-2-2-2-2-20000000000000000000000000000000000002-22-20000
χ2822222-2-22-22-2222220000222222222222220000-2-2-2-200-200000000-2-2-2-2-2000000000000000000000000000000000000-22-220000
χ2922222-2-22-22-2222-2-20000-2-22222-2-2-2-2-2-2-2-20000-2-22200-200000000-22222000000000000000000000000000000002i−2i2i−2i00000000
χ3022222-2-22-22-2222-2-20000-2-22222-2-2-2-2-2-2-2-20000-2-22200-200000000-2222200000000000000000000000000000000−2i2i−2i2i00000000
χ312222-2-222-2-22-2-220022220022-2-20000000000002-200-2-2-2000000002000022-2-222-2-22−22−22−22−22−22−22−22−22−22−22−22−2000000000000
χ322222-2-222-2-22-2-220022220022-2-20000000000002-200-2-2-2000000002000022-2-222-2-2−22−22−22−22−22−22−22−22−22−22−22−22000000000000
χ332222-2-222-2-22-2-2200-2-2-2-20022-2-20000000000002-20022-20000000020000-2-222-2-2222−22−2−22−222−22−22−22−2−22−22−22−22000000000000
χ342222-2-222-2-22-2-2200-2-2-2-20022-2-20000000000002-20022-20000000020000-2-222-2-222−22−222−22−2−22−22−22−222−22−22−22−2000000000000
χ352222-2-22-1-2-2211-100222200-1-11133−3−333−3−30000-1100-2-2133−3−333−3−3-13−33−3-1-111-1-1112−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ362222-2-22-1-2-2211-100222200-1-11133−3−333−3−30000-1100-2-2133−3−333−3−3-13−33−3-1-111-1-111−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ372222-2-22-1-2-2211-100222200-1-111−3−333−3−3330000-1100-2-21−3−333−3−333-1−33−33-1-111-1-1112−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ382222-2-22-1-2-2211-100222200-1-111−3−333−3−3330000-1100-2-21−3−333−3−333-1−33−33-1-111-1-111−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ392222-2-22-1-2-2211-100-2-2-2-200-1-11133−3−333−3−30000-1100221−3−333−3−333-13−33−311-1-111-1-12−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ402222-2-22-1-2-2211-100-2-2-2-200-1-11133−3−333−3−30000-1100221−3−333−3−333-13−33−311-1-111-1-1−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ412222-2-22-1-2-2211-100-2-2-2-200-1-111−3−333−3−3330000-110022133−3−333−3−3-1−33−3311-1-111-1-12−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ422222-2-22-1-2-2211-100-2-2-2-200-1-111−3−333−3−3330000-110022133−3−333−3−3-1−33−3311-1-111-1-1−22−222−22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ4322-2-22-2-222-222220022-2-200-2-2-2-2000000000000-2-200-222000000002000022-2-2-2-222−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-2-22-2-222-222220022-2-200-2-2-2-2000000000000-2-200-222000000002000022-2-2-2-222i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-2-22-2-222-2222200-2-22200-2-2-2-2000000000000-2-2002-220000000020000-2-22222-2-2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4622-2-22-2-222-2222200-2-22200-2-2-2-2000000000000-2-2002-220000000020000-2-22222-2-2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4722-2-22-2-2-12-22-1-1-10022-2-200111133−3−3−3−33300001100-22-133−3−3−3−333-13−3−33-1-11111-1-1−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
χ4822-2-22-2-2-12-22-1-1-10022-2-200111133−3−3−3−33300001100-22-133−3−3−3−333-13−3−33-1-11111-1-1i2−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
χ4922-2-22-2-2-12-22-1-1-10022-2-2001111−3−33333−3−300001100-22-1−3−33333−3−3-1−333−3-1-11111-1-1−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
χ5022-2-22-2-2-12-22-1-1-10022-2-2001111−3−33333−3−300001100-22-1−3−33333−3−3-1−333−3-1-11111-1-1i2−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
χ5122-2-22-2-2-12-22-1-1-100-2-22200111133−3−3−3−333000011002-2-1−3−33333−3−3-13−3−3311-1-1-1-111−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
χ5222-2-22-2-2-12-22-1-1-100-2-22200111133−3−3−3−333000011002-2-1−3−33333−3−3-13−3−3311-1-1-1-111i2−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
χ5322-2-22-2-2-12-22-1-1-100-2-222001111−3−33333−3−3000011002-2-133−3−3−3−333-1−333−311-1-1-1-111−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
χ5422-2-22-2-2-12-22-1-1-100-2-222001111−3−33333−3−3000011002-2-133−3−3−3−333-1−333−311-1-1-1-111i2−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
χ5522-2-2-22-22-222-2-22-2-222-2-222-2-222-2-2-2-22222-2-222-22-222-2-2-2-2-2-222222-2-2222222-2-2-2-2000000000000000000000000000000000000
χ5622-2-2-22-22-222-2-22-2-2-2-22222-2-222-2-2-2-2222222-2-2-22-22-22-22222-2-2-2-22-2-222-2-2-2-22222000000000000000000000000000000000000
χ5722-2-2-22-2-1-22211-12222-2-2-2-211-1-1-1-1-1-1111122-2-21-12-22-21-1-1-1-11111-1-1-111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000
χ5822-2-2-22-2-1-22211-12222-2-2-2-211-1-1-1-1-1-1111122-2-21-12-22-21-1-1-1-11111-1-1-111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000
χ5922-2-2-22-2-1-22211-122-2-222-2-211-1-1-1-1-1-11111-2-2221-12-2-2211111-1-1-1-1-1-1-1111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ6022-2-2-22-2-1-22211-122-2-222-2-211-1-1-1-1-1-11111-2-2221-12-2-2211111-1-1-1-1-1-1-1111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000
χ6122-2-2-22-2-1-22211-1-2-222-2-22211-1-11111-1-1-1-1-2-2221-1-222-211111-1-1-1-1-111-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ6222-2-2-22-2-1-22211-1-2-222-2-22211-1-11111-1-1-1-1-2-2221-1-222-211111-1-1-1-1-111-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ6322-2-2-22-2-1-22211-1-2-2-2-2222211-1-11111-1-1-1-122-2-21-1-22-221-1-1-1-11111-111-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ6422-2-2-22-2-1-22211-1-2-2-2-2222211-1-11111-1-1-1-122-2-21-1-22-221-1-1-1-11111-111-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ6522-2-2-2-22222-2-2-22220000-2-2-2-2222222-2-2-2-200002-2-2200200000000-2-2-2220000000000000000000000000000000000002i−2i−2i2i0000
χ6622-2-2-2-22222-2-2-22220000-2-2-2-2222222-2-2-2-200002-2-2200200000000-2-2-222000000000000000000000000000000000000−2i2i2i−2i0000
χ6722-2-2-2-22222-2-2-22-2-2000022-2-222-2-2-2-2222200002-22-200200000000-222-2-2000000000000000000000000000000002-2-2200000000
χ6822-2-2-2-22222-2-2-22-2-2000022-2-222-2-2-2-2222200002-22-200200000000-222-2-200000000000000000000000000000000-222-200000000
χ6944444-4-4-2-44-4-2-2-244000044-2-2-2-2-2-2-2-2-2-2-2-2000022-4-4002000000002222200000000000000000000000000000000000000000000
χ7044444-4-4-2-44-4-2-2-2-4-40000-4-4-2-2-2-22222222200002244002000000002-2-2-2-200000000000000000000000000000000000000000000
χ714444-44-444-4-4-4-440000000044-4-4000000000000-440000400000000-4000000000000000000000000000000000000000000000000
χ724444-44-4-24-4-422-200000000-2-2222323−23−232323−23−2300002-20000-2000000002−2323−232300000000000000000000000000000000000000000000
χ734444-44-4-24-4-422-200000000-2-222−23−232323−23−23232300002-20000-200000000223−2323−2300000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.