Finite Group Databasebeta

← Group #13138751

Character table — Group #13138751

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12224444366612121212882424242433666666121212121212121236661212121224242424242424242424242424242424444488888888444488121212121212121212121212242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i1-11-1i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii-11-11i−i-1-11111-1-1-1-111−i−iii−i−iiiii−i−i
χ111111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111ii−i−i−i−iii1-1-11−ii-1-111-1-11111-1-1−i−iiiii−i−i−i−iii
χ121111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111−i−iiiii−i−i-111-1−ii11-1-1-1-111-1-111ii−i−i−i−iii−i−iii
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−iii−i−iii−i−i−i−iiiii11-1-1ii−i−iii−i−i-11-11−ii-1-11111-1-1-1-111ii−i−iii−i−i−i−iii
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−iii−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii1-11-1−ii11-1-111-1-111-1-1−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−iii−i−iii−i−i−i−iiiii-1-111ii−i−i−i−iii-111-1i−i11-1-1-1-111-1-111−i−iiiii−i−iii−i−i
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−iii−i−iii−i−i−i−iiiii-1-111−i−iiiii−i−i1-1-11i−i-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i
χ1722222222222222222222222-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002222000022000000000000-1-1-1-10000-1-1-1-10000
χ1822222222222222222222222-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000-2-20000000000001111000011110000
χ192222222222222222222222-12-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000220000-1-1-1-1000000000000-1-1-1-1
χ202222222222222222222222-12-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000-2-2000011110000000000001111
χ212222222222222222-2-2-2-2-2-22-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-11111-2-2-2-211111111000022220000-2-200000000000011110000-1-1-1-10000
χ222222222222222222-2-2-2-2-2-22-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-2-2-2000022000000000000-1-1-1-1000011110000
χ232222222222222222-2-2-2-2-2-2-12-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111112222000000000000-2-20000-1-1-1-10000000000001111
χ242222222222222222-2-2-2-2-2-2-12-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-20000000000002200001111000000000000-1-1-1-1
χ252222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-12-122-1-1-2-21111-2-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii00002i2i−2i−2i00002-2000000000000-1-1110000−i−iii0000
χ262222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-12-122-1-1-2-21111-2-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000−2i−2i2i2i0000-2200000000000011-1-10000ii−i−i0000
χ272222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-12-12-1-12211-2-2-2-211-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii22-2-20000000000002i−2i0000-1-111000000000000−i−iii
χ282222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-12-12-1-12211-2-2-2-211-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii-2-222000000000000−2i2i000011-1-1000000000000ii−i−i
χ292222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-12-122-1-1-2-21111-2-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i00002i2i−2i−2i0000-2200000000000011-1-10000−i−iii0000
χ302222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-12-122-1-1-2-21111-2-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000−2i−2i2i2i00002-2000000000000-1-1110000ii−i−i0000
χ312222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-12-12-1-12211-2-2-2-211-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i22-2-2000000000000−2i2i0000-1-111000000000000ii−i−i
χ322222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-12-12-1-12211-2-2-2-211-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i-2-2220000000000002i−2i000011-1-1000000000000−i−iii
χ3322-2-222-2-222-2-222-2-20000002222-2-2-2-222-2-222-2-22-2-2222-2-2000000000000000000002-22-2000000000000000000000000002-22-20000
χ3422-2-222-2-222-2-222-2-20000002222-2-2-2-222-2-222-2-22-2-2222-2-200000000000000000000-22-2200000000000000000000000000-22-220000
χ3522-2-222-2-222-2-222-2-20000002-12-1-2-2112211-1-1-2-2-111-1-1-1113−33−3000033−3−333−3−300002-22-20000000000000000003−33−30000-11-110000
χ3622-2-222-2-222-2-222-2-20000002-12-1-2-2112211-1-1-2-2-111-1-1-1113−33−3000033−3−333−3−30000-22-22000000000000000000−33−3300001-11-10000
χ3722-2-222-2-222-2-222-2-20000002-12-1-2-2112211-1-1-2-2-111-1-1-111−33−330000−3−333−3−33300002-22-2000000000000000000−33−330000-11-110000
χ3822-2-222-2-222-2-222-2-20000002-12-1-2-2112211-1-1-2-2-111-1-1-111−33−330000−3−333−3−3330000-22-220000000000000000003−33−300001-11-10000
χ3922-2-2-2-22222-2-2-2-2220000002222-2-2-2-2-2-222-2-2222-2-22-2-222000000000000000000002i−2i−2i2i000000000000000000000000002i−2i−2i2i0000
χ4022-2-2-2-22222-2-2-2-2220000002222-2-2-2-2-2-222-2-2222-2-22-2-22200000000000000000000−2i2i2i−2i00000000000000000000000000−2i2i2i−2i0000
χ4122-2-2-2-22222-2-2-2-2220000002-12-1-2-211-2-2-1-11122-111-111-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i300002i−2i−2i2i000000000000000000−333−30000−iii−i0000
χ4222-2-2-2-22222-2-2-2-2220000002-12-1-2-211-2-2-1-11122-111-111-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i30000−2i2i2i−2i0000000000000000003−3−330000i−i−ii0000
χ4322-2-2-2-22222-2-2-2-2220000002-12-1-2-211-2-2-1-11122-111-111-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i300002i−2i−2i2i0000000000000000003−3−330000−iii−i0000
χ4422-2-2-2-22222-2-2-2-2220000002-12-1-2-211-2-2-1-11122-111-111-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i30000−2i2i2i−2i000000000000000000−333−30000i−i−ii0000
χ452-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-2-22-22-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ462-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-2-22-22-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ472-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ482-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ492-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-2-2-22-222i−2i−2i2i2i−2i−2i2i2-22-22i−2i−2i2i00000000000000002i−2i2-20000000000000000002i−2i2-20000000000000000
χ502-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-2-2-22-222i−2i−2i2i2i−2i−2i2i2-22-22i−2i−2i2i0000000000000000−2i2i-22000000000000000000−2i2i-220000000000000000
χ512-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−ii−2i2i2i−2ii−i-11-11−iii−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ232i−2i2-2000000000000000000−ii-11000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ522-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−ii−2i2i2i−2ii−i-11-11−iii−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−2i2i-22000000000000000000i−i1-1000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ532-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−ii−2i2i2i−2ii−i-11-11−iii−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232i−2i2-2000000000000000000−ii-11000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ542-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−ii−2i2i2i−2ii−i-11-11−iii−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−2i2i-22000000000000000000i−i1-1000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ552-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-2-2-22-22−2i2i2i−2i−2i2i2i−2i2-22-2−2i2i2i−2i00000000000000002i−2i-220000000000000000002i−2i-220000000000000000
χ562-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-2-2-22-22−2i2i2i−2i−2i2i2i−2i2-22-2−2i2i2i−2i0000000000000000−2i2i2-2000000000000000000−2i2i2-20000000000000000
χ572-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-21-1-22i−i2i−2i−2i2i−ii-11-11i−i−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132i−2i-22000000000000000000−ii1-1000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ582-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-21-1-22i−i2i−2i−2i2i−ii-11-11i−i−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−2i2i2-2000000000000000000i−i-11000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ592-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-21-1-22i−i2i−2i−2i2i−ii-11-11i−i−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ132i−2i-22000000000000000000−ii1-1000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ602-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-21-1-22i−i2i−2i−2i2i−ii-11-11i−i−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−2i2i2-2000000000000000000i−i-11000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
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−2i2i2i−2i−2i2i2iiiii−i−i−i−i000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4−4i4i−4i−4i4i4i-2-2-2-2-2-2-2-2222222221111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000000000
χ6544-4-444-4-444-4-444-4-4000000-24-2422-4-4-2-2-4-44422-222-2-2-2220000000000000000000000000000000000000000000000000000000000
χ6644-4-444-4-444-4-444-4-4000000-2-2-2-22222-2-222-2-2221-1-1111-1-123−2323−230000−3−333−3−333000000000000000000000000000000000000000000
χ6744-4-444-4-444-4-444-4-4000000-2-2-2-22222-2-222-2-2221-1-1111-1-1−2323−2323000033−3−333−3−3000000000000000000000000000000000000000000
χ6844-4-4-4-44444-4-4-4-444000000-24-2422-4-42244-4-4-2-2-222-222-2-20000000000000000000000000000000000000000000000000000000000
χ6944-4-4-4-44444-4-4-4-444000000-2-2-2-2222222-2-222-2-21-1-11-1-111−2i32i32i3−2i30000i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000000000
χ7044-4-4-4-44444-4-4-4-444000000-2-2-2-2222222-2-222-2-21-1-11-1-1112i3−2i3−2i32i30000−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000000000
χ714-44-44i−4i4i−4i4-44-44i−4i4i−4i0000004-2-424-4-224i−4i−2i2i−2i2i4i−4i-2-222−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ724-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-242-4-224-4−2i2i4i−4i4i−4i−2i2i-2-222−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ734-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-222-22-22−2i2i−2i2i−2i2i−2i2i11-1-1i−ii−i000000003ζ7+3ζ23−3ζ7−3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ133ζ5+3ζ13−3ζ5−3ζ13000000000000000000000000000000000000000000
χ744-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-222-22-22−2i2i−2i2i−2i2i−2i2i11-1-1i−ii−i00000000−3ζ7−3ζ233ζ7+3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ13−3ζ5−3ζ133ζ5+3ζ13000000000000000000000000000000000000000000
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χ1011212-12-121212-12-12-6-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-12-121212-6-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121212i−12i−12i12i-666-6−6i6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212−12i12i12i−12i-666-66i−6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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