Finite Group Databasebeta

← Group #13138931

Character table — Group #13138931

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222444436661212121288242424243366666612121212121212123666121212122424242424242424242424242424242444448888888822446666881212121212121212242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-11111-1-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-11111i−i-1-111-1-1-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii-1-111-1-1-1-1i−i1111-1-111−i−iiiii−i−i−i−iii
χ111111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−i−i−iii1-1-1111-1-1−ii-1-1-1-11111ii−i−i−i−iii−i−iii
χ121111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iiiii−i−i-111-1-1-111−ii11-1-111-1-1−i−iii−i−iiiii−i−i
χ131111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i-1-111-1-1-1-1−ii1111-1-111ii−i−i−i−iiiii−i−i
χ141111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-11111−ii-1-111-1-1-1-1−i−iii−i−iii−i−iii
χ151111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i−i−iii-111-1-1-111i−i11-1-111-1-1ii−i−iii−i−i−i−iii
χ161111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iiiii−i−i1-1-1111-1-1i−i-1-1-1-11111−i−iiiii−i−iii−i−i
χ1722222222222222222222222-1-1-1222-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000000002222020200-1-100000000-1-100000000-1-1-1-1
χ1822222222222222222222222-1-1-1222-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20-20-200110000000011000000001111
χ192222222222222222222222-1222-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1222200000000000000002200-1-1-1-1000000-1-1-1-10000
χ202222222222222222222222-1222-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-200111100000011110000
χ212222222222222222-2-2-2-2-2-22-1-1-1222-122-1-122-1-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000000022220-20-20011000000001100000000-1-1-1-1
χ222222222222222222-2-2-2-2-2-22-1-1-1222-122-1-122-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000-2-2-2-2020200-1-100000000-1-1000000001111
χ232222222222222222-2-2-2-2-2-2-1222-1-1-12-1-122-1-122-1-1-1-1-1-1-1-111-2-211-2-21111111122220000000000000000-2-200-1-1-1-100000011110000
χ242222222222222222-2-2-2-2-2-2-1222-1-1-12-1-122-1-122-1-1-1-1-1-1-1-111-2-211-2-211111111-2-2-2-2000000000000000022001111000000-1-1-1-10000
χ252222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-1-1-1222-1-2-211-2-211-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii000000002i2i−2i−2i020-200-1-1000000001100000000−i−iii
χ262222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-1-1-1222-1-2-211-2-211-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii00000000−2i−2i2i2i0-202001100000000-1-100000000ii−i−i
χ272222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-1222-1-1-1211-2-211-2-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii22-2-200000000000000002i−2i00-1-111000000−i−iii0000
χ282222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-1222-1-1-1211-2-211-2-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii-2-2220000000000000000−2i2i0011-1-1000000ii−i−i0000
χ292222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-1222-1-2-211-2-211-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i000000002i2i−2i−2i0-202001100000000-1-100000000−i−iii
χ302222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-1222-1-2-211-2-211-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i00000000−2i−2i2i2i020-200-1-1000000001100000000ii−i−i
χ312222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-1222-1-1-1211-2-211-2-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i22-2-20000000000000000−2i2i00-1-111000000ii−i−i0000
χ322222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-1222-1-1-1211-2-211-2-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i-2-22200000000000000002i−2i0011-1-1000000−i−iii0000
χ3322-2-22i−2i2i−2i22-2-22i−2i2i−2i000000222-2-22-2-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ3422-2-22i−2i2i−2i22-2-22i−2i2i−2i000000222-2-22-2-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ3522-2-2−2i2i−2i2i22-2-2−2i2i−2i2i000000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ3622-2-2−2i2i−2i2i22-2-2−2i2i−2i2i000000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ372-22-22i−2i−2i2i2-22-2−2i2i2i−2i00000022-22-2-22-22i−2i2i−2i−2i2i−2i2i2-22-22i−2i−2i2i00000000000000002-22i−2i000000000000000000002-22i−2i00000000000000
χ382-22-22i−2i−2i2i2-22-2−2i2i2i−2i00000022-22-2-22-22i−2i2i−2i−2i2i−2i2i2-22-22i−2i−2i2i0000000000000000-22−2i2i00000000000000000000-22−2i2i00000000000000
χ392-22-22i−2i−2i2i2-22-2−2i2i2i−2i000000-12-2211-1-2−ii2i−2ii−i−2i2i-11-11−iii−iζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ2300ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ232-22i−2i00000000000000000000-11−ii000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ402-22-22i−2i−2i2i2-22-2−2i2i2i−2i000000-12-2211-1-2−ii2i−2ii−i−2i2i-11-11−iii−iζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ2300ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23-22−2i2i000000000000000000001-1i−i000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ412-22-22i−2i−2i2i2-22-2−2i2i2i−2i000000-12-2211-1-2−ii2i−2ii−i−2i2i-11-11−iii−i−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ232-22i−2i00000000000000000000-11−ii000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ422-22-22i−2i−2i2i2-22-2−2i2i2i−2i000000-12-2211-1-2−ii2i−2ii−i−2i2i-11-11−iii−i−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23-22−2i2i000000000000000000001-1i−i000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ432-22-2−2i2i2i−2i2-22-22i−2i−2i2i00000022-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i2i−2i00000000000000002-2−2i2i000000000000000000002-2−2i2i00000000000000
χ442-22-2−2i2i2i−2i2-22-22i−2i−2i2i00000022-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i2i−2i0000000000000000-222i−2i00000000000000000000-222i−2i00000000000000
χ452-22-2−2i2i2i−2i2-22-22i−2i−2i2i000000-12-2211-1-2i−i−2i2i−ii2i−2i-11-11i−i−ii−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ132-2−2i2i00000000000000000000-11i−i000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ462-22-2−2i2i2i−2i2-22-22i−2i−2i2i000000-12-2211-1-2i−i−2i2i−ii2i−2i-11-11i−i−ii−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-222i−2i000000000000000000001-1−ii000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ472-22-2−2i2i2i−2i2-22-22i−2i−2i2i000000-12-2211-1-2i−i−2i2i−ii2i−2i-11-11i−i−iiζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ1300ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ132-2−2i2i00000000000000000000-11i−i000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ482-22-2−2i2i2i−2i2-22-22i−2i−2i2i000000-12-2211-1-2i−i−2i2i−ii2i−2i-11-11i−i−iiζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ1300ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-222i−2i000000000000000000001-1−ii000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ492-2-2222-2-22-2-22-2-22200000022-2-22-2-222222-2-2-2-22-2-2222-2-20000000000000000000000002i−2i2i−2i000000000000000000000000002i−2i2i−2i
χ502-2-2222-2-22-2-22-2-22200000022-2-22-2-222222-2-2-2-22-2-2222-2-2000000000000000000000000−2i2i−2i2i00000000000000000000000000−2i2i−2i2i
χ512-2-2222-2-22-2-22-2-2220000002-1112-2-2-122-1-1-2-211-111-1-1-111003−3003−33−33−33−33−3000000002i−2i2i−2i000000−i3i300000000−i3i300000000−ii−ii
χ522-2-2222-2-22-2-22-2-2220000002-1112-2-2-122-1-1-2-211-111-1-1-111003−3003−33−33−33−33−300000000−2i2i−2i2i000000i3−i300000000i3−i300000000i−ii−i
χ532-2-2222-2-22-2-22-2-2220000002-1112-2-2-122-1-1-2-211-111-1-1-11100−3300−33−33−33−33−33000000002i−2i2i−2i000000i3−i300000000i3−i300000000−ii−ii
χ542-2-2222-2-22-2-22-2-2220000002-1112-2-2-122-1-1-2-211-111-1-1-11100−3300−33−33−33−33−3300000000−2i2i−2i2i000000−i3i300000000−i3i300000000i−ii−i
χ552-2-22-2-2222-2-2222-2-200000022-2-22-2-22-2-2-2-222222-2-22-2-2220000000000000000000000002-2-22000000000000000000000000002-2-22
χ562-2-22-2-2222-2-2222-2-200000022-2-22-2-22-2-2-2-222222-2-22-2-222000000000000000000000000-222-200000000000000000000000000-222-2
χ572-2-22-2-2222-2-2222-2-20000002-1112-2-2-1-2-21122-1-1-111-111-1-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i3000000002-2-22000000−i3i300000000i3−i300000000-111-1
χ582-2-22-2-2222-2-2222-2-20000002-1112-2-2-1-2-21122-1-1-111-111-1-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i300000000-222-2000000i3−i300000000−i3i3000000001-1-11
χ592-2-22-2-2222-2-2222-2-20000002-1112-2-2-1-2-21122-1-1-111-111-1-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i3000000002-2-22000000i3−i300000000−i3i300000000-111-1
χ602-2-22-2-2222-2-2222-2-20000002-1112-2-2-1-2-21122-1-1-111-111-1-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i300000000-222-2000000−i3i300000000i3−i3000000001-1-11
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ634444-4-4-4-44444-4-4-4-44i−4i4i4i−4i−4i-2-2-2-2-2-2-2-2222222221111-1-1-1-1−2i−2i−2i−2i2i2i2i2iiiii−i−i−i−i000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4−4i4i−4i−4i4i4i-2-2-2-2-2-2-2-2222222221111-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000000000
χ6544-4-44i−4i4i−4i44-4-44i−4i4i−4i0000004-2-22-44-424i−4i−2i2i4i−4i−2i2i-2-222−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ6644-4-44i−4i4i−4i44-4-44i−4i4i−4i000000-244-42-22-4−2i2i4i−4i−2i2i4i−4i-2-222−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ6744-4-44i−4i4i−4i44-4-44i−4i4i−4i000000-2-2-222-222−2i2i−2i2i−2i2i−2i2i11-1-1i−ii−i000000003ζ7+3ζ23−3ζ7−3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ133ζ5+3ζ13−3ζ5−3ζ13000000000000000000000000000000000000000000
χ6844-4-44i−4i4i−4i44-4-44i−4i4i−4i000000-2-2-222-222−2i2i−2i2i−2i2i−2i2i11-1-1i−ii−i00000000−3ζ7−3ζ233ζ7+3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ13−3ζ5−3ζ133ζ5+3ζ13000000000000000000000000000000000000000000
χ6944-4-4−4i4i−4i4i44-4-4−4i4i−4i4i0000004-2-22-44-42−4i4i2i−2i−4i4i2i−2i-2-2222i−2i2i−2i0000000000000000000000000000000000000000000000000000000000
χ7044-4-4−4i4i−4i4i44-4-4−4i4i−4i4i000000-244-42-22-42i−2i−4i4i2i−2i−4i4i-2-2222i−2i2i−2i0000000000000000000000000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i44-4-4−4i4i−4i4i000000-2-2-222-2222i−2i2i−2i2i−2i2i−2i11-1-1−ii−ii00000000−3ζ5−3ζ133ζ5+3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ7+3ζ23−3ζ7−3ζ23−3ζ7−3ζ233ζ7+3ζ23000000000000000000000000000000000000000000
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χ10112-1212-1212i−12i−12i12i-66-666i−6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12−12i12i12i−12i-66-66−6i6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-12121212-12-12-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212-12-121212-666-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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