Finite Group Databasebeta

← Group #10690284

Character table — Group #10690284

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order122244442234466612121212224444446612121212121212121212446688888888121212121212242424242424242424242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-111ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-111ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-111−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-111−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222222222-2-222-2-222-2-2-2-222-2-2-2-2-2-22200000000-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-222-2-20000000022-2-22200000000000000000000000000000000
χ192222222222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000000000000000
χ212222222222-122-1-1-1-1-1-1-122-2-222-2-2-1-11111-1-11111-2-2-1-10000000011-1-11133−3−333−3−333−3−333−3−30000000000000000
χ222222222222-122-1-1-1-1-1-1-122-2-222-2-2-1-11111-1-11111-2-2-1-10000000011-1-111−3−333−3−333−3−333−3−3330000000000000000
χ232222222222-122-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2112222-2-2-2-2111111-1-1-1-1-1-1-1-1111111110000000000000000
χ242222222222-122-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-2222211111111111111-1-1-1-1-1-1-1-10000000000000000
χ252222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111221100000000-1-111-1-133−3−333−3−3−3−333−3−3330000000000000000
χ262222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111221100000000-1-111-1-1−3−333−3−33333−3−333−3−30000000000000000
χ2722222222-2-22-2-22222222002-2002-2-2-222-2-2-2-222-2-20000000000000000000000000000000000000000002-22-20000
χ2822222222-2-22-2-22222222002-2002-2-2-222-2-2-2-222-2-2000000000000000000000000000000000000000000-22-220000
χ2922222222-2-22-2-2222222200-2200-22-2-2-2-222-2-2-2-22200000000000000000000000000000000000000000000002-22-2
χ3022222222-2-22-2-2222222200-2200-22-2-2-2-222-2-2-2-2220000000000000000000000000000000000000000000000-22-22
χ312222-2-2-2-2222-2-2222-2-2-2-222-2-2-2-22222-2-2-2-2-2-22222-222200000000-2-2-2-22200000000000000000000000000000000
χ322222-2-2-2-2222-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222222-2-2-2000000002222-2-200000000000000000000000000000000
χ332222-2-2-2-222-1-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-11111112-2-1-12i2i−2i−2i2i2i−2i−2i-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ342222-2-2-2-222-1-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-11111112-2-1-1−2i−2i2i2i−2i−2i2i2i-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ352222-2-2-2-222-1-2-2-1-1-1111122-2-2-2-222-1-1111111-1-1-1-1-22-1-1000000001111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ362222-2-2-2-222-1-2-2-1-1-1111122-2-2-2-222-1-1111111-1-1-1-1-22-1-1000000001111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ372222-2-2-2-222-1-2-2-1-1-11111-2-22222-2-2-1-1-1-1-1-1111111-22112i2i−2i−2i−2i−2i2i2i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ382222-2-2-2-222-1-2-2-1-1-11111-2-22222-2-2-1-1-1-1-1-1111111-2211−2i−2i2i2i2i2i−2i−2i11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ392222-2-2-2-222-1-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-12-21100000000-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ402222-2-2-2-222-1-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-12-21100000000-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ412222-2-2-2-2-2-2222222-2-2-2-2002-200-22-2-222-2-222-2-2220000000000000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-2222222-2-2-2-2002-200-22-2-222-2-222-2-222000000000000000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-2222222-2-2-2-200-22002-2-2-2-2-2222222-2-200000000000000000000000000000000000000000000002i−2i−2i2i
χ442222-2-2-2-2-2-2222222-2-2-2-200-22002-2-2-2-2-2222222-2-20000000000000000000000000000000000000000000000−2i2i2i−2i
χ452-2-2222-2-2-2222-22-2-222-2-22-2002-2002-200002-20000002-2−i2i2−i2i2−i2i2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ462-2-2222-2-2-2222-22-2-222-2-22-2002-2002-200002-20000002-2i2−i2i2−i2i2−i2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ472-2-2222-2-2-2222-22-2-222-2-2-2200-22002-200002-2000000-22−i2i2−i2i2i2−i2i2−i200-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ482-2-2222-2-2-2222-22-2-222-2-2-2200-22002-200002-2000000-22i2−i2i2−i2−i2i2−i2i200-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ492-2-2222-2-2-22-12-2-111-1-1112-2002-200-113−33−3-113−33−300-11−i2i2−i2i2−i2i2−i2i23−3-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ502-2-2222-2-2-22-12-2-111-1-1112-2002-200-113−33−3-113−33−300-11i2−i2i2−i2i2−i2i2−i23−3-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ512-2-2222-2-2-22-12-2-111-1-1112-2002-200-11−33−33-11−33−3300-11−i2i2−i2i2−i2i2−i2i2−33-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ522-2-2222-2-2-22-12-2-111-1-1112-2002-200-11−33−33-11−33−3300-11i2−i2i2−i2i2−i2i2−i2−33-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ532-2-2222-2-2-22-12-2-111-1-111-2200-2200-113−33−3-113−33−3001-1−i2i2−i2i2i2−i2i2−i2−331-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ542-2-2222-2-2-22-12-2-111-1-111-2200-2200-113−33−3-113−33−3001-1i2−i2i2−i2−i2i2−i2i2−331-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ552-2-2222-2-2-22-12-2-111-1-111-2200-2200-11−33−33-11−33−33001-1−i2i2−i2i2i2−i2i2−i23−31-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ562-2-2222-2-2-22-12-2-111-1-111-2200-2200-11−33−33-11−33−33001-1i2−i2i2−i2−i2i2−i2i23−31-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ572-2-22-2-222-222-222-2-2-2-2222-200-22002-20000-220000002-22−2−222−2−2200-22002−22−2−22−222−22−2−22−220000000000000000
χ582-2-22-2-222-222-222-2-2-2-2222-200-22002-20000-220000002-2−222−2−222−200-2200−22−222−22−2−22−222−22−20000000000000000
χ592-2-22-2-222-222-222-2-2-2-222-22002-2002-20000-22000000-222−2−22−222−2002-2002−22−2−22−22−22−222−22−20000000000000000
χ602-2-22-2-222-222-222-2-2-2-222-22002-2002-20000-22000000-22−222−22−2−22002-200−22−222−22−22−22−2−22−220000000000000000
χ612-2-22-2-222-22-1-22-11111-1-12-200-2200-113−33−31-1−33−3300-112−2−222−2−223−31-1−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ622-2-22-2-222-22-1-22-11111-1-12-200-2200-113−33−31-1−33−3300-11−222−2−222−23−31-1−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ632-2-22-2-222-22-1-22-11111-1-12-200-2200-11−33−331-13−33−300-112−2−222−2−22−331-13−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ642-2-22-2-222-22-1-22-11111-1-12-200-2200-11−33−331-13−33−300-11−222−2−222−2−331-13−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ652-2-22-2-222-22-1-22-11111-1-1-22002-200-113−33−31-1−33−33001-12−2−22−222−2−33-113−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ662-2-22-2-222-22-1-22-11111-1-1-22002-200-113−33−31-1−33−33001-1−222−22−2−22−33-113−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ672-2-22-2-222-22-1-22-11111-1-1-22002-200-11−33−331-13−33−3001-12−2−22−222−23−3-11−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ682-2-22-2-222-22-1-22-11111-1-1-22002-200-11−33−331-13−33−3001-1−222−22−2−223−3-11−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ6944444444-4-4-2-4-4-2-2-2-2-2-2-2004-4004-422-2-22222-2-22200000000000000000000000000000000000000000000000000
χ7044444444-4-4-2-4-4-2-2-2-2-2-2-200-4400-442222-2-22222-2-200000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-4-4-244-2-2-22222004-400-4422-2-222-2-222-2-200000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-4-4-244-2-2-2222200-44004-42222-2-2-2-2-2-22200000000000000000000000000000000000000000000000000
χ7344-4-44i−4i4i−4i00400-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000002-22i−2i000000000000
χ7444-4-44i−4i4i−4i00400-44-44i−4i4i−4i000000000000000000000000000000000000000000000000000000-22−2i2i000000000000
χ7544-4-4−4i4i−4i4i00400-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000002-2−2i2i000000000000
χ7644-4-4−4i4i−4i4i00400-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000000000-222i−2i000000000000
χ774-44-44i−4i−4i4i00400-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000002-22i−2i00000000
χ784-44-44i−4i−4i4i00400-4-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000-22−2i2i00000000
χ794-44-4−4i4i4i−4i00400-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000002-2−2i2i00000000
χ804-44-4−4i4i4i−4i00400-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000-222i−2i00000000
χ814-4-4444-4-44-44-444-4-444-4-400000000-440000-44000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-44-4-2-44-222-2-222000000002-223−23−23232-223−23−232300000000000000000000000000000000000000000000000000
χ834-4-4444-4-44-4-2-44-222-2-222000000002-2−232323−232-2−232323−2300000000000000000000000000000000000000000000000000
χ844-4-44-4-4444-444-44-4-4-4-44400000000-4400004-4000000000000000000000000000000000000000000000000000000
χ854-4-44-4-4444-4-24-4-22222-2-2000000002-223−23−2323-22−232323−2300000000000000000000000000000000000000000000000000
χ864-4-44-4-4444-4-24-4-22222-2-2000000002-2−232323−23-2223−23−232300000000000000000000000000000000000000000000000000
χ8788-8-88i−8i8i−8i00-4004-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8−8i8i−8i8i00-4004-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-88i−8i−8i8i00-40044-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i8i−8i00-40044-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000

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