Finite Group Databasebeta

← Group #10691113

Character table — Group #10691113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888888888888888881212121224242424242448484848
order12222234444446661212121244444446612121212121212121212448888888812121212121212122424242424242424242424242424242444444444444488
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
χ4522-2-22-22-22-2002-22-20000002i−2i2i−2i02-2002-2002-200002−22−2−i2i2−i2i22i−2i002i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000000000
χ4622-2-22-22-22-2002-22-20000002i−2i2i−2i02-2002-2002-20000−22−22i2−i2i2−i22i−2i002i−2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000000000
χ4722-2-22-22-22-2002-22-2000000−2i2i−2i2i02-2002-2002-200002−22−2i2−i2i2−i2−2i2i00−2i2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000000000
χ4822-2-22-22-22-2002-22-2000000−2i2i−2i2i02-2002-2002-20000−22−22−i2i2−i2i2−2i2i00−2i2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000000000
χ4922-2-22-2-1-22-20021-1133−3−3002i−2i2i−2i0-113−3-113−3-113−3002−22−2−i2i2−i2i2−ii−i3i3−ii−i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000
χ5022-2-22-2-1-22-20021-1133−3−3002i−2i2i−2i0-113−3-113−3-113−300−22−22i2−i2i2−i2−ii−i3i3−ii−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000
χ5122-2-22-2-1-22-20021-1133−3−300−2i2i−2i2i0-113−3-113−3-113−3002−22−2i2−i2i2−i2i−ii3−i3i−ii3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000
χ5222-2-22-2-1-22-20021-1133−3−300−2i2i−2i2i0-113−3-113−3-113−300−22−22−i2i2−i2i2i−ii3−i3i−ii3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000
χ5322-2-22-2-1-22-20021-11−3−333002i−2i2i−2i0-11−33-11−33-11−33002−22−2−i2i2−i2i2−iii3−i3−iii3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000
χ5422-2-22-2-1-22-20021-11−3−333002i−2i2i−2i0-11−33-11−33-11−3300−22−22i2−i2i2−i2−iii3−i3−iii3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000
χ5522-2-22-2-1-22-20021-11−3−33300−2i2i−2i2i0-11−33-11−33-11−33002−22−2i2−i2i2−i2i−i−i3i3i−i−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000
χ5622-2-22-2-1-22-20021-11−3−33300−2i2i−2i2i0-11−33-11−33-11−3300−22−22−i2i2−i2i2i−i−i3i3i−i−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000
χ5722-2-2-222-2-22002-22-20000002i−2i−2i2i0-22002-200-220000−i2i2i2−i2−222−22i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000000000
χ5822-2-2-222-2-22002-22-20000002i−2i−2i2i0-22002-200-220000i2−i2−i2i22−2−222i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000000000
χ5922-2-2-222-2-22002-22-2000000−2i2i2i−2i0-22002-200-220000−i2i2i2−i22−2−22−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000000000
χ6022-2-2-222-2-22002-22-2000000−2i2i2i−2i0-22002-200-220000i2−i2−i2i2−222−2−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000000000
χ6122-2-2-22-1-2-220021-1133−3−3002i−2i−2i2i01-1−33-11−331-13−300−i2i2i2−i2−222−2−iii3−i3i−i−i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000
χ6222-2-2-22-1-2-220021-1133−3−3002i−2i−2i2i01-1−33-11−331-13−300i2−i2−i2i22−2−22−iii3−i3i−i−i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000
χ6322-2-2-22-1-2-220021-1133−3−300−2i2i2i−2i01-1−33-11−331-13−300−i2i2i2−i22−2−22i−i−i3i3−iii3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000
χ6422-2-2-22-1-2-220021-1133−3−300−2i2i2i−2i01-1−33-11−331-13−300i2−i2−i2i2−222−2i−i−i3i3−iii3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000
χ6522-2-2-22-1-2-220021-11−3−333002i−2i−2i2i01-13−3-113−31-1−3300−i2i2i2−i2−222−2−ii−i3i3i−ii3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000
χ6622-2-2-22-1-2-220021-11−3−333002i−2i−2i2i01-13−3-113−31-1−3300i2−i2−i2i22−2−22−ii−i3i3i−ii3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000
χ6722-2-2-22-1-2-220021-11−3−33300−2i2i2i−2i01-13−3-113−31-1−3300−i2i2i2−i22−2−22i−ii3−i3−ii−i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000
χ6822-2-2-22-1-2-220021-11−3−33300−2i2i2i−2i01-13−3-113−31-1−3300i2−i2−i2i2−222−2i−ii3−i3−ii−i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000
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
χ7344-4-44-444-4400-4-44-4000000000004-400-4400-4400000000000000000000000000000000000000000000000000
χ7444-4-44-4-24-4400-42-222323−23−230000000-2223−232-2−23232-2−2323000000000000000000000000000000000000000000000000
χ7544-4-44-4-24-4400-42-22−23−2323230000000-22−23232-223−232-223−23000000000000000000000000000000000000000000000000
χ7644-4-4-44444-400-4-44-400000000000-4400-44004-400000000000000000000000000000000000000000000000000
χ7744-4-4-44-244-400-42-222323−23−2300000002-2−23232-223−23-22−2323000000000000000000000000000000000000000000000000
χ7844-4-4-44-244-400-42-22−23−23232300000002-223−232-2−2323-2223−23000000000000000000000000000000000000000000000000
χ794-4-440040004i−4i0-4-444i−4i4i−4i000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000
χ804-4-440040004i−4i0-4-444i−4i4i−4i00000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000
χ814-4-44004000−4i4i0-4-44−4i4i−4i4i000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000
χ824-4-44004000−4i4i0-4-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000
χ838-88-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-4000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000000
χ858-88-800-4000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-40008i−8i044-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-4000−8i8i044-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000

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