Finite Group Databasebeta

← Group #10713690

Character table — Group #10713690

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222222244444444444444444444444444444444888888888888888888888888242424242424242448484848
order1222223444466688888888121212122424242424242424444466888812121212121212121212242424242424242424242424444488881212121212121212242424242424242416161616161616162244
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
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91-1-11-111-111-11-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101-1-11-111-111-11-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111-1-11-111-111-11-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121-1-11-111-111-11-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-111-11-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131-1-11-111-111-11-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-111-1-11-1-1-1-1-111111-1-1111111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141-1-11-111-111-11-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-111-1-11-1-1-1-1-111111-1-1111111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151-1-11-111-111-11-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-111-1-11-1-1-1-1-111111-1-1111111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161-1-11-111-111-11-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-111-1-11-1-1-1-1-111111-1-1111111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-22222-2-2222222222222-2-2-2-222-2-2222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
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
χ19222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ21222222-12222-1-1-122-2-2-2-222-1-1-1-111111111-2-2-2-2-1-122-2-2-111111111-11111-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ22222222-12222-1-1-122-2-2-2-222-1-1-1-111111111-2-2-2-2-1-122-2-2-111111111-11111-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ23222222-12222-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-222-111111111-1-1-1-1-11111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ24222222-12222-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-222-111111111-1-1-1-1-11111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ25222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ26222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ272222-2-2222-2-222222000022-2-2-2-2000000000000-2-2-2-2002000000002000022-2-222-2-22-22-200002-22-22-22-200000000000000000000
χ282222-2-2222-2-222222000022-2-2-2-2000000000000-2-2-2-2002000000002000022-2-222-2-2-22-220000-22-22-22-2200000000000000000000
χ292222-2-2222-2-2222-2-20000-2-2-2-2-2-2000000000000-2-2220020000000020000-2-222-2-22200002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000
χ302222-2-2222-2-2222-2-20000-2-2-2-2-2-2000000000000-2-2220020000000020000-2-222-2-2220000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000
χ312222-2-22-2-222222002222002222222222220000-2-200-2-2-200000000-2-2-2-2-2000000000000000000000000000000002−22−22−22−20000
χ322222-2-22-2-222222002222002222222222220000-2-200-2-2-200000000-2-2-2-2-200000000000000000000000000000000−22−22−22−220000
χ332222-2-22-2-22222200-2-2-2-2002222-2-2-2-2-2-2-2-20000-2-20022-200000000-22222000000000000000000000000000000002−22−2−22−220000
χ342222-2-22-2-22222200-2-2-2-2002222-2-2-2-2-2-2-2-20000-2-20022-200000000-2222200000000000000000000000000000000−22−222−22−20000
χ352222-2-2-122-2-2-1-1-122000022111133−3−333−3−3000011-2-200-133−3−333−3−3-13−33−3-1-111-1-1112-22-20000-11-11-11-113−3−333−3−33000000000000
χ362222-2-2-122-2-2-1-1-122000022111133−3−333−3−3000011-2-200-133−3−333−3−3-13−33−3-1-111-1-111-22-2200001-11-11-11-1−333−3−333−3000000000000
χ372222-2-2-122-2-2-1-1-1220000221111−3−333−3−333000011-2-200-1−3−333−3−333-1−33−33-1-111-1-1112-22-20000-11-11-11-11−333−3−333−3000000000000
χ382222-2-2-122-2-2-1-1-1220000221111−3−333−3−333000011-2-200-1−3−333−3−333-1−33−33-1-111-1-111-22-2200001-11-11-11-13−3−333−3−33000000000000
χ392222-2-2-122-2-2-1-1-1-2-20000-2-2111133−3−333−3−30000112200-1−3−333−3−333-13−33−311-1-111-1-100002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii000000000000
χ402222-2-2-122-2-2-1-1-1-2-20000-2-2111133−3−333−3−30000112200-1−3−333−3−333-13−33−311-1-111-1-10000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i000000000000
χ412222-2-2-122-2-2-1-1-1-2-20000-2-21111−3−333−3−3330000112200-133−3−333−3−3-1−33−3311-1-111-1-100002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii000000000000
χ422222-2-2-122-2-2-1-1-1-2-20000-2-21111−3−333−3−3330000112200-133−3−333−3−3-1−33−3311-1-111-1-10000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i000000000000
χ432-2-222-222-22-22-2-20022-2-20022-2-22222-2-2-2-200002-200-22200000000-2-2-22200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ442-2-222-222-22-22-2-20022-2-20022-2-22222-2-2-2-200002-200-22200000000-2-2-22200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ452-2-222-222-22-22-2-200-2-2220022-2-2-2-2-2-2222200002-2002-2200000000-222-2-200000000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ462-2-222-222-22-22-2-200-2-2220022-2-2-2-2-2-2222200002-2002-2200000000-222-2-200000000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ472-2-222-22-22-222-2-2220000-2-2-2-2220000000000002-2-2200-2000000002000022-2-2-2-2222i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ482-2-222-22-22-222-2-2220000-2-2-2-2220000000000002-2-2200-2000000002000022-2-2-2-222−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ492-2-222-22-22-222-2-2-2-2000022-2-2220000000000002-22-200-20000000020000-2-22222-2-200002-2-22000000002-22-2-22-22000000000000
χ502-2-222-22-22-222-2-2-2-2000022-2-2220000000000002-22-200-20000000020000-2-22222-2-20000-222-200000000-22-222-22-2000000000000
χ512-2-222-2-1-22-22-111220000-2-211-1-133−3−3−3−3330000-11-2200133−3−3−3−333-13−3−33-1-11111-1-12i−2i−2i2i0000−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i3000000000000
χ522-2-222-2-1-22-22-111220000-2-211-1-133−3−3−3−3330000-11-2200133−3−3−3−333-13−3−33-1-11111-1-1−2i2i2i−2i0000i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i3000000000000
χ532-2-222-2-1-22-22-111220000-2-211-1-1−3−33333−3−30000-11-22001−3−33333−3−3-1−333−3-1-11111-1-12i−2i−2i2i0000−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i3000000000000
χ542-2-222-2-1-22-22-111220000-2-211-1-1−3−33333−3−30000-11-22001−3−33333−3−3-1−333−3-1-11111-1-1−2i2i2i−2i0000i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i3000000000000
χ552-2-222-2-1-22-22-111-2-200002211-1-133−3−3−3−3330000-112-2001−3−33333−3−3-13−3−3311-1-1-1-11100002-2-22−333−33−3−33-11-111-11-1000000000000
χ562-2-222-2-1-22-22-111-2-200002211-1-133−3−3−3−3330000-112-2001−3−33333−3−3-13−3−3311-1-1-1-1110000-222-23−3−33−333−31-11-1-11-11000000000000
χ572-2-222-2-1-22-22-111-2-200002211-1-1−3−33333−3−30000-112-200133−3−3−3−333-1−333−311-1-1-1-11100002-2-223−3−33−333−3-11-111-11-1000000000000
χ582-2-222-2-1-22-22-111-2-200002211-1-1−3−33333−3−30000-112-200133−3−3−3−333-1−333−311-1-1-1-1110000-222-2−333−33−3−331-11-1-11-11000000000000
χ592-2-22-222-222-22-2-2-2-222-2-22222-2-22222-2-2-2-2-2-222-22-222-2-2-2-2-2-22222222-2-2-2-2-2-22222000000000000000000000000000000000000
χ602-2-22-222-222-22-2-2-2-2-2-2222222-2-2-2-2-2-2222222-2-2-22-22-22-22222-2-2-2-22-2-222-2-2-2-22222000000000000000000000000000000000000
χ612-2-22-22-1-222-2-1112222-2-2-2-2-1-111-1-1-1-1111122-2-21-12-22-21-1-1-1-11111-1-1-111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000
χ622-2-22-22-1-222-2-1112222-2-2-2-2-1-111-1-1-1-1111122-2-21-12-22-21-1-1-1-11111-1-1-111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000
χ632-2-22-22-1-222-2-11122-2-222-2-2-1-1111111-1-1-1-1-2-2221-12-2-2211111-1-1-1-1-111-1-1-1-1-1-111112i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ642-2-22-22-1-222-2-11122-2-222-2-2-1-1111111-1-1-1-1-2-2221-12-2-2211111-1-1-1-1-111-1-1-1-1-1-11111−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000
χ652-2-22-22-1-222-2-111-2-222-2-222-1-111-1-1-1-11111-2-2221-1-222-211111-1-1-1-1-1-1-1111111-1-1-1-10000000033−3−3−3−33333−3−3−3−333000000000000
χ662-2-22-22-1-222-2-111-2-222-2-222-1-111-1-1-1-11111-2-2221-1-222-211111-1-1-1-1-1-1-1111111-1-1-1-100000000−3−33333−3−3−3−33333−3−3000000000000
χ672-2-22-22-1-222-2-111-2-2-2-22222-1-1111111-1-1-1-122-2-21-1-22-221-1-1-1-11111-111-1-11111-1-1-1-10000000033−3−3−3−333−3−33333−3−3000000000000
χ682-2-22-22-1-222-2-111-2-2-2-22222-1-1111111-1-1-1-122-2-21-1-22-221-1-1-1-11111-111-1-11111-1-1-1-100000000−3−33333−3−333−3−3−3−333000000000000
χ694444444-4-4-4-444400000000-4-4-4-4000000000000440000-400000000-4000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-20000000022222323−23−232323−23−230000-2-200002000000002−2323−232300000000000000000000000000000000000000000000
χ71444444-2-4-4-4-4-2-2-2000000002222−23−232323−23−2323230000-2-20000200000000223−2323−2300000000000000000000000000000000000000000000
χ724444-4-4-2-4-444-2-2-200444400-2-2-2-2-2-2-2-2-2-2-2-200002200-4-42000000002222200000000000000000000000000000000000000000000
χ734444-4-4-2-4-444-2-2-200-4-4-4-400-2-2-2-22222222200002200442000000002-2-2-2-200000000000000000000000000000000000000000000
χ7444-4-40040000-44-422−22−2i22i2−2i22i222−220000−2i22i2−2i22i2−2i22i2−2i22i22i−2i2i−2i00000002i−2i2i−2i2i−2i2i−2i0000022−220022−2200000000000000000000000000000000000000
χ7544-4-40040000-44-422−222i2−2i22i2−2i222−2200002i2−2i22i2−2i22i2−2i22i2−2i2−2i2i−2i2i0000000−2i2i−2i2i−2i2i−2i2i0000022−220022−2200000000000000000000000000000000000000
χ7644-4-40040000-44-4−2222−2i22i2−2i22i2−22220000−2i22i2−2i22i2−2i22i2−2i22i2−2i2i−2i2i0000000−2i2i−2i2i−2i2i−2i2i00000−222200−222200000000000000000000000000000000000000
χ7744-4-40040000-44-4−22222i2−2i22i2−2i2−222200002i2−2i22i2−2i22i2−2i22i2−2i22i−2i2i−2i00000002i−2i2i−2i2i−2i2i−2i00000−222200−222200000000000000000000000000000000000000
χ7844-4-400-200002-2222−22−2i22i2−2i22i222−2223−2323−232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232i−2i2i−2i0000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000−226−6−226−6000000000000000000000000000000000000
χ7944-4-400-200002-2222−22−2i22i2−2i22i222−22−2323−23232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72i−2i2i−2i0000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000−22−66−22−66000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.