Finite Group Databasebeta

← Group #10691127

Character table — Group #10691127

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888888888888888881212121224242424242448484848
order12222234444446661212121244444446612121212121212121212448888888812121212121212122424242424242424242424242424242444444444442488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1
χ91111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−ii−iii−i−i1-11-1
χ101111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−ii−i−iii-11-11
χ111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−ii−iii−i−i-11-11
χ121111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−ii−i−iii1-11-1
χ131111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-11ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−ii−i−i−iii1-1-11
χ141111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-11ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iii−iiii−i−i-111-1
χ151111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-11−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−ii−i−i−iii-111-1
χ161111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-11−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iii−iiii−i−i1-1-11
χ172222222222-2-22222-2-2-2-2-2-22222-222-2-222-2-222-2-2-2-20000000022-2-222-2-2000000000000000000000000000000
χ182222222222-2-22222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-22200000000-2-222-2-222000000000000000000000000000000
χ192222222-2-2-222-222222222-20000-22222-2-2-2-2-2-2-2-200000000000000000000000000000000002222-2-200000000
χ202222222-2-2-222-222222222-20000-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-22200000000
χ212222222-2-2-2-2-2-2222-2-2-2-2-220000222-2-2-2-222-2-22200000000000000000000000000000000000000002-22-20000
χ222222222-2-2-2-2-2-2222-2-2-2-2-220000222-2-2-2-222-2-2220000000000000000000000000000000000000000-22-220000
χ23222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ24222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000
χ25222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000
χ26222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000
χ27222222-1222-2-22-1-1-11111-2-22222-2-1-111-1-111-1-111-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−300000000000000
χ28222222-1222-2-22-1-1-11111-2-22222-2-1-111-1-111-1-111-2-200000000-1-111-1-111−3−333−3−333−3−333−3−33300000000000000
χ29222222-1222-2-22-1-1-11111-2-2-2-2-2-2-2-1-111-1-111-1-111220000000011-1-111-1-133−3−333−3−3−3−333−3−33300000000000000
χ30222222-1222-2-22-1-1-11111-2-2-2-2-2-2-2-1-111-1-111-1-111220000000011-1-111-1-1−3−333−3−33333−3−333−3−300000000000000
χ312222-2-222-2-22222222222-2-222-2-22-2-2-2-222-2-2-2-222-220000000022-2-2-2-222000000000000000000000000000000
χ322222-2-222-2-22222222222-2-2-2-2222-2-2-2-222-2-2-2-2222-200000000-2-22222-2-2000000000000000000000000000000
χ332222-2-22-22222-22222222-220000-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-22-22222-22222222-220000-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-22-222-2-2-2222-2-2-2-22-200002-2-222-2-2-2-2222200000000000000000000000000000000002i2i−2i−2i−2i2i00000000
χ362222-2-22-222-2-2-2222-2-2-2-22-200002-2-222-2-2-2-222220000000000000000000000000000000000−2i−2i2i2i2i−2i00000000
χ372222-2-2-12-2-2222-1-1-1-1-1-1-1-2-222-2-221111-1-11111-1-1-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ382222-2-2-12-2-2222-1-1-1-1-1-1-1-2-222-2-221111-1-11111-1-1-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ392222-2-2-12-2-2222-1-1-1-1-1-1-1-2-2-2-22221111-1-11111-1-12-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ402222-2-2-12-2-2222-1-1-1-1-1-1-1-2-2-2-22221111-1-11111-1-12-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ412222-2-2-12-2-2-2-22-1-1-111112222-2-2-211-1-1-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000000000
χ422222-2-2-12-2-2-2-22-1-1-111112222-2-2-211-1-1-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000000000
χ432222-2-2-12-2-2-2-22-1-1-1111122-2-222-211-1-1-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ442222-2-2-12-2-2-2-22-1-1-1111122-2-222-211-1-1-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ452-2-222-22-22-2002-22-20000002-22-202-2002-2002-20000−i2i2−i2i2−i2i2−i2i22-2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ462-2-222-22-22-2002-22-20000002-22-202-2002-2002-20000i2−i2i2−i2i2−i2i2−i22-2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ472-2-222-22-22-2002-22-2000000-22-2202-2002-2002-20000−i2i2−i2i2i2−i2i2−i2-2200-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ482-2-222-22-22-2002-22-2000000-22-2202-2002-2002-20000i2−i2i2−i2−i2i2−i2i2-2200-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ492-2-222-2-1-22-20021-1133−3−3002-22-20-113−3-113−3-113−300−i2i2−i2i2−i2i2−i2i2-113−3-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000
χ502-2-222-2-1-22-20021-1133−3−3002-22-20-113−3-113−3-113−300i2−i2i2−i2i2−i2i2−i2-113−3-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000
χ512-2-222-2-1-22-20021-1133−3−300-22-220-113−3-113−3-113−300−i2i2−i2i2i2−i2i2−i21-1−331-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000
χ522-2-222-2-1-22-20021-1133−3−300-22-220-113−3-113−3-113−300i2−i2i2−i2−i2i2−i2i21-1−331-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000
χ532-2-222-2-1-22-20021-11−3−333002-22-20-11−33-11−33-11−3300−i2i2−i2i2−i2i2−i2i2-11−33-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000
χ542-2-222-2-1-22-20021-11−3−333002-22-20-11−33-11−33-11−3300i2−i2i2−i2i2−i2i2−i2-11−33-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000
χ552-2-222-2-1-22-20021-11−3−33300-22-220-11−33-11−33-11−3300−i2i2−i2i2i2−i2i2−i21-13−31-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000
χ562-2-222-2-1-22-20021-11−3−33300-22-220-11−33-11−33-11−3300i2−i2i2−i2−i2i2−i2i21-13−31-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000
χ572-2-22-222-2-22002-22-20000002-2-220-22002-200-2200002−2−222−2−222-200-22002−22−2−22−222−22−2−22−2200000000000000
χ582-2-22-222-2-22002-22-20000002-2-220-22002-200-220000−222−2−222−22-200-2200−22−222−22−2−22−222−22−200000000000000
χ592-2-22-222-2-22002-22-2000000-222-20-22002-200-2200002−2−22−222−2-22002-2002−22−2−22−22−22−222−22−200000000000000
χ602-2-22-222-2-22002-22-2000000-222-20-22002-200-220000−222−22−2−22-22002-200−22−222−22−22−22−2−22−2200000000000000
χ612-2-22-22-1-2-220021-1133−3−3002-2-2201-1−33-11−331-13−3002−2−222−2−22-11−331-13−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000
χ622-2-22-22-1-2-220021-1133−3−3002-2-2201-1−33-11−331-13−300−222−2−222−2-11−331-13−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000
χ632-2-22-22-1-2-220021-1133−3−300-222-201-1−33-11−331-13−3002−2−22−222−21-13−3-11−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000
χ642-2-22-22-1-2-220021-1133−3−300-222-201-1−33-11−331-13−300−222−22−2−221-13−3-11−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000
χ652-2-22-22-1-2-220021-11−3−333002-2-2201-13−3-113−31-1−33002−2−222−2−22-113−31-1−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000
χ662-2-22-22-1-2-220021-11−3−333002-2-2201-13−3-113−31-1−3300−222−2−222−2-113−31-1−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000
χ672-2-22-22-1-2-220021-11−3−33300-222-201-13−3-113−31-1−33002−2−22−222−21-1−33-113−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000
χ682-2-22-22-1-2-220021-11−3−33300-222-201-13−3-113−31-1−3300−222−22−2−221-1−33-113−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000
χ69444444-2-4-4-444-4-2-2-2-2-2-2-24-40000-4-2-2-2-222222222000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-4-4-2-2-22222-4400004-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ714444-4-4-2-44444-4-2-2-2-2-2-2-2-440000-4222222-2-2-2-222000000000000000000000000000000000000000000000000
χ724444-4-4-2-444-4-4-4-2-2-222224-40000422-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ734-44-40040004i−4i0-4-444i−4i4i−4i000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000
χ744-44-40040004i−4i0-4-444i−4i4i−4i00000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000
χ754-44-4004000−4i4i0-4-44−4i4i−4i4i000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000
χ764-44-4004000−4i4i0-4-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000
χ774-4-444-444-4400-4-44-4000000000004-400-4400-4400000000000000000000000000000000000000000000000000
χ784-4-444-4-24-4400-42-222323−23−230000000-2223−232-2−23232-2−2323000000000000000000000000000000000000000000000000
χ794-4-444-4-24-4400-42-22−23−2323230000000-22−23232-223−232-223−23000000000000000000000000000000000000000000000000
χ804-4-44-44444-400-4-44-400000000000-4400-44004-400000000000000000000000000000000000000000000000000
χ814-4-44-44-244-400-42-222323−23−2300000002-2−23232-223−23-22−2323000000000000000000000000000000000000000000000000
χ824-4-44-44-244-400-42-22−23−23232300000002-223−232-2−2323-2223−23000000000000000000000000000000000000000000000000
χ8388-8-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-800-4000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000000
χ8588-8-800-4000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-40008i−8i044-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-4000−8i8i044-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000

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