Finite Group Databasebeta

← Group #10691577

Character table — Group #10691577

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888888888888888881212121224242424242448484848
order12222234444446661212121244466888812121212121212121212888888888824242424242424242424242424242424242424242424242422442488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1
χ911111111-1-11-1-111111111-1-111ii−i−i11-1-1-1-1-1-1-1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-1ii−i−i1-1i−i
χ1011111111-1-11-1-111111111-1-111ii−i−i11-1-1-1-1-1-1-1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-11−i−iii-11−ii
χ1111111111-1-11-1-111111111-1-111ii−i−i11-1-1-1-1-1-1-1-1i−i-1-111−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-11-1ii−i−i-11−ii
χ1211111111-1-11-1-111111111-1-111ii−i−i11-1-1-1-1-1-1-1-1i−i-1-111−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-11−i−iii1-1i−i
χ1311111111-1-11-1-111111111-1-111−i−iii11-1-1-1-1-1-1-1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−i−iii1-1−ii
χ1411111111-1-11-1-111111111-1-111−i−iii11-1-1-1-1-1-1-1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-11ii−i−i-11i−i
χ1511111111-1-11-1-111111111-1-111−i−iii11-1-1-1-1-1-1-1-1−ii-1-111ii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1−i−iii-11i−i
χ1611111111-1-11-1-111111111-1-111−i−iii11-1-1-1-1-1-1-1-1−ii-1-111ii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-11ii−i−i1-1−ii
χ172222222-222-222222-2-2-2-2-2-2-2222222-2-222-2-222-2-2-2-2000000000000000022-2-222-2-20000000000000000000000
χ182222222-222-222222-2-2-2-2-2-2-222-2-2-2-2-2-222-2-222-2-2220000000000000000-2-222-2-2220000000000000000000000
χ192222222-2-2-2-2-2-2222-2-2-2-2-222222i2i−2i−2i-2-2-2-222-2-222−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ202222222-2-2-2-2-2-2222-2-2-2-2-22222−2i−2i2i2i-2-2-2-222-2-2222i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000
χ25222222-12-2-22-2-2-1-1-1-1-1-1-12-2-2-1-12i2i−2i−2i-1-1111111112i−2i22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000000000
χ26222222-12-2-22-2-2-1-1-1-1-1-1-12-2-2-1-12i2i−2i−2i-1-1111111112i−2i-2-222−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ27222222-12-2-22-2-2-1-1-1-1-1-1-12-2-2-1-1−2i−2i2i2i-1-111111111−2i2i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000000000
χ28222222-12-2-22-2-2-1-1-1-1-1-1-12-2-2-1-1−2i−2i2i2i-1-111111111−2i2i-2-2222i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ29222222-1-222-222-1-1-11111-2-2-2-1-1222211-1-111-1-111-2-20000000033−3−333−3−3-1-111-1-11133−3−333−3−300000000000000
χ30222222-1-222-222-1-1-11111-2-2-2-1-1222211-1-111-1-111-2-200000000−3−333−3−333-1-111-1-111−3−333−3−33300000000000000
χ31222222-1-222-222-1-1-11111-2-2-2-1-1-2-2-2-211-1-111-1-111220000000033−3−333−3−311-1-111-1-1−3−333−3−33300000000000000
χ32222222-1-222-222-1-1-11111-2-2-2-1-1-2-2-2-211-1-111-1-1112200000000−3−333−3−33311-1-111-1-133−3−333−3−300000000000000
χ33222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i1111-1-111-1-1−2i2i0000000033−3−3−3−333−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000000
χ34222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i1111-1-111-1-1−2i2i00000000−3−33333−3−3−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000000000
χ35222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i1111-1-111-1-12i−2i0000000033−3−3−3−333ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000000
χ36222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i1111-1-111-1-12i−2i00000000−3−33333−3−3ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000000000
χ372222-2-2222-222-22222222-2-22-2-20000-2-222-2-2-2-222000000000000000000000000000000000022-2-2-2200000000
χ382222-2-2222-222-22222222-2-22-2-20000-2-222-2-2-2-2220000000000000000000000000000000000-2-2222-200000000
χ392222-2-222-222-222222222-22-2-2-20000-2-2-2-22222-2-200000000000000000000000000000000002222-2-200000000
χ402222-2-222-222-222222222-22-2-2-20000-2-2-2-22222-2-20000000000000000000000000000000000-2-2-2-22200000000
χ412222-2-22-22-2-22-2222-2-2-2-222-2-2-20000222222-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i0000
χ422222-2-22-22-2-22-2222-2-2-2-222-2-2-20000222222-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i0000
χ432222-2-22-2-22-2-22222-2-2-2-22-22-2-2000022-2-2-2-2222200000000000000000000000000000000000000002-2-220000
χ442222-2-22-2-22-2-22222-2-2-2-22-22-2-2000022-2-2-2-222220000000000000000000000000000000000000000-222-20000
χ452-2-222-220220-2-22-2-200000002-22i−2i2i−2i002-2002-200002−22−2−i2i2−i2i22−22−22−22−22i−2i002i−2i00−i2i2−i2i2−i2i2−i2i200000000000000
χ462-2-222-220220-2-22-2-200000002-22i−2i2i−2i002-2002-20000−22−22i2−i2i2−i2−22−22−22−222i−2i002i−2i00i2−i2i2−i2i2−i2i2−i200000000000000
χ472-2-222-220220-2-22-2-200000002-2−2i2i−2i2i002-2002-200002−22−2i2−i2i2−i22−22−22−22−2−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i200000000000000
χ482-2-222-220220-2-22-2-200000002-2−2i2i−2i2i002-2002-20000−22−22−i2i2−i2i2−22−22−22−22−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i200000000000000
χ492-2-222-220-2-20222-2-200000002-22-2-2200-2200-2200002−2−22−222−22−22−2−22−222-200-2200−22−222−22−200000000000000
χ502-2-222-220-2-20222-2-200000002-22-2-2200-2200-220000−222−22−2−22−22−222−22−22-200-22002−22−2−22−2200000000000000
χ512-2-222-220-2-20222-2-200000002-2-222-200-2200-2200002−2−222−2−222−22−2−22−22-22002-2002−22−2−22−2200000000000000
χ522-2-222-220-2-20222-2-200000002-2-222-200-2200-220000−222−2−222−2−22−222−22−2-22002-200−22−222−22−200000000000000
χ532-2-222-2-10220-2-2-1113−33−3000-112i−2i2i−2i3−3-113−3-113−3002−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ii−i3i3−ii−i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000
χ542-2-222-2-10220-2-2-1113−33−3000-112i−2i2i−2i3−3-113−3-113−300−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ii−i3i3−ii−i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000
χ552-2-222-2-10220-2-2-1113−33−3000-11−2i2i−2i2i3−3-113−3-113−3002−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23i−ii3−i3i−ii3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000
χ562-2-222-2-10220-2-2-1113−33−3000-11−2i2i−2i2i3−3-113−3-113−300−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23i−ii3−i3i−ii3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000
χ572-2-222-2-10220-2-2-111−33−33000-112i−2i2i−2i−33-11−33-11−33002−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−iii3−i3−iii3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000
χ582-2-222-2-10220-2-2-111−33−33000-112i−2i2i−2i−33-11−33-11−3300−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−iii3−i3−iii3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000
χ592-2-222-2-10220-2-2-111−33−33000-11−2i2i−2i2i−33-11−33-11−33002−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7i−i−i3i3i−i−i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000
χ602-2-222-2-10220-2-2-111−33−33000-11−2i2i−2i2i−33-11−33-11−3300−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7i−i−i3i3i−i−i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000
χ612-2-222-2-10-2-2022-1113−33−3000-112-2-223−31-1−331-1−33002−2−22−222−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23-11−331-13−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000
χ622-2-222-2-10-2-2022-1113−33−3000-112-2-223−31-1−331-1−3300−222−22−2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-11−331-13−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000
χ632-2-222-2-10-2-2022-1113−33−3000-11-222-23−31-1−331-1−33002−2−222−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ231-13−3-11−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000
χ642-2-222-2-10-2-2022-1113−33−3000-11-222-23−31-1−331-1−3300−222−2−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ231-13−3-11−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000
χ652-2-222-2-10-2-2022-111−33−33000-112-2-22−331-13−31-13−3002−2−22−222−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7-113−31-1−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000
χ662-2-222-2-10-2-2022-111−33−33000-112-2-22−331-13−31-13−300−222−22−2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7-113−31-1−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000
χ672-2-222-2-10-2-2022-111−33−33000-11-222-2−331-13−31-13−3002−2−222−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ71-1−33-113−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000
χ682-2-222-2-10-2-2022-111−33−33000-11-222-2−331-13−31-13−300−222−2−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ71-1−33-113−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000
χ694444-4-4-244-444-4-2-2-2-2-2-2-2-4-4422000022-2-22222-2-2000000000000000000000000000000000000000000000000
χ704444-4-4-24-444-44-2-2-2-2-2-2-2-44-42200002222-2-2-2-222000000000000000000000000000000000000000000000000
χ714444-4-4-2-44-4-44-4-2-2-2222244-4220000-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ724444-4-4-2-4-44-4-44-2-2-222224-44220000-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ7344-4-4004400-400-44-444-4-4000000000000000000000000000000000000000000000000000004-4000000000000
χ7444-4-4004400-400-44-444-4-400000000000000000000000000000000000000000000000000000-44000000000000
χ7544-4-4004-400400-44-4-4-44400000000000000000000000000000000000000000000000000000004i−4i0000000000
χ7644-4-4004-400400-44-4-4-4440000000000000000000000000000000000000000000000000000000−4i4i0000000000
χ774-4-44-44404-40-444-4-40000000-440000004-400-4400000000000000000000000000000000000000000000000000
χ784-4-44-4440-4404-44-4-40000000-44000000-44004-400000000000000000000000000000000000000000000000000
χ794-4-44-44-204-40-44-22223−2323−230002-20000−2323-22−23232-223−23000000000000000000000000000000000000000000000000
χ804-4-44-44-204-40-44-222−2323−23230002-2000023−23-2223−232-2−2323000000000000000000000000000000000000000000000000
χ814-4-44-44-20-4404-4-22223−2323−230002-20000−23232-223−23-22−2323000000000000000000000000000000000000000000000000
χ824-4-44-44-20-4404-4-222−2323−23230002-2000023−232-2−2323-2223−23000000000000000000000000000000000000000000000000
χ8388-8-800-4800-8004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-8008004-4444-4-40000000000000000000000000000000000000000000000000000000000000000000
χ858-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

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