Finite Group Databasebeta

← Group #13155413

Character table — Group #13155413

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order12223334466666666612121212333666666666121212121212121212121212224412121212366612121212121244666666668812121212121212121212242424242424242424242424242424241212121212124444881212121224242424121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-11-11-111-1-11-1-111-111-1-1i−i11-1-111-1-1i−i1-1ii−i−i11-1-1ii−i−iiiiiii−i−i−i−i−i−ii−iii−i−ii−i1-1i−iii−i−iii−i−i1-11-1
χ101-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-11-11-111-1-11-1-111-111-1-1i−i11-1-111-1-1−ii1-1ii−i−i11-1-1−i−iii−i−i−i−i−i−iiiiiiii−iii−i−ii−i-11−iiii−i−i−i−iii-11-11
χ111-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-11-11-111-1-11-1-111-111-1-1−ii11-1-111-1-1i−i1-1−i−iii11-1-1ii−i−iiiiiii−i−i−i−i−i−i−ii−i−iii−ii-11i−i−i−iiiii−i−i-11-11
χ121-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-11-11-111-1-11-1-111-111-1-1−ii11-1-111-1-1−ii1-1−i−iii11-1-1−i−iii−i−i−i−i−i−iiiiiii−ii−i−iii−ii1-1−ii−i−iii−i−iii1-11-1
χ131-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-1-11-11-1-1111-1-111-111-1-1i−i-1-111-1-111i−i-11ii−i−i-1-111ii−i−iiiiiii−i−i−i−i−i−ii−iii−i−i−ii1-1−ii−i−iii−i−iii1-1-11
χ141-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-1-11-11-1-1111-1-111-111-1-1i−i-1-111-1-111−ii-11ii−i−i-1-111−i−iii−i−i−i−i−i−iiiiiiii−iii−i−i−ii-11i−i−i−iiiii−i−i-111-1
χ151-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-1-11-11-1-1111-1-111-111-1-1−ii-1-111-1-111i−i-11−i−iii-1-111ii−i−iiiiiii−i−i−i−i−i−i−ii−i−iiii−i-11−iiii−i−i−i−iii-111-1
χ161-1-111111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1111-11-111111-1-1-1-1-1-11-11-1-1111-1-111-111-1-1−ii-1-111-1-111−ii-11−i−iii-1-111−i−iii−i−i−i−i−i−iiiiiii−ii−i−iiii−i1-1i−iii−i−iii−i−i1-1-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-2002222222200-2-20000-2-2-2-20000000000000000000000000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-200-2-2-2-2-2-2-2-20022000022220000000000000000000000000000000000000000
χ19222222-1222222-12-1-1222222-1-122-1-1-12-1-1-1-1-1222-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-12-1-1-1-1-10022-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1220000-1-1-1-100000000
χ20222222-1222222-12-1-1222222-1-122-1-1-12-1-1-1-1-1222-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22-12-1-1-1-1-100221111-1-1-1-10000000000000000-2-21111-2-20000111100000000
χ21222222-1222222-12-1-1222222-1-122-1-1-12-1-1-1-1-1222-1-1-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-122-21-21111100-2-2-1-1-1-11111000000000000000022-1-1-1-1-2-20000111100000000
χ22222222-1222222-12-1-1222222-1-122-1-1-12-1-1-1-1-1222-1-1-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-21-21111100-2-2111111110000000000000000-2-21111220000-1-1-1-100000000
χ23222222-1-2-22222-12-1-12-2-2-2-22-1-122-1-1-12-1-1-111-2-2-21111-2-2-222-2-21111-1-1-1-1111111002-12-1-1-1-1-100-2-2−i3i3−i3i31111000000000000000000−i3i3−i3i3000000−i3i3−i3i300000000
χ24222222-1-2-22222-12-1-12-2-2-2-22-1-122-1-1-12-1-1-111-2-2-21111-2-2-222-2-21111-1-1-1-1111111002-12-1-1-1-1-100-2-2i3−i3i3−i31111000000000000000000i3−i3i3−i3000000i3−i3i3−i300000000
χ25222222-1-2-22222-12-1-12-2-2-2-22-1-122-1-1-12-1-1-111-2-2-21111-2-2-2-2-222-1-1-1-1-1-1-1-111111100-21-2111110022−i3i3−i3i3-1-1-1-1000000000000000000−i3i3−i3i3000000i3−i3i3−i300000000
χ26222222-1-2-22222-12-1-12-2-2-2-22-1-122-1-1-12-1-1-111-2-2-21111-2-2-2-2-222-1-1-1-1-1-1-1-111111100-21-2111110022i3−i3i3−i3-1-1-1-1000000000000000000i3−i3i3−i3000000−i3i3−i3i300000000
χ2722222-12222-1-1-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-100-12-12-1-1-1-122-1-10000-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000220000-1-1-1-10000
χ2822222-12222-1-1-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-100-12-12-1-1-1-1-2-2-1-10000-1-1-1-11111-2-21111-2-211110000000000-2-2000011110000
χ2922222-12222-1-1-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1001-21-21111221100001111-1-1-1-122-1-1-1-122-1-1-1-10000000000-2-2000011110000
χ3022222-12222-1-1-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1001-21-21111-2-211000011111111-2-21111-2-211110000000000220000-1-1-1-10000
χ3122222-12-2-22-1-1-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-2-2-2-2-2-2-1-1-1-1-2-2111100-12-12-1-1-1-10011000011113−33−30033−3−30033−3−300000000000000003−33−30000
χ3222222-12-2-22-1-1-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-2-2-2-2-2-2-1-1-1-1-2-2111100-12-12-1-1-1-1001100001111−33−3300−3−33300−3−3330000000000000000−33−330000
χ3322222-12-2-22-1-1-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2222222-1-1-1-1-2-21111001-21-2111100-1-10000-1-1-1-13−33−30033−3−30033−3−30000000000000000−33−330000
χ3422222-12-2-22-1-1-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2222222-1-1-1-1-2-21111001-21-2111100-1-10000-1-1-1-1−33−3300−3−33300−3−33300000000000000003−33−30000
χ352222-12222-12222-122-12222-1-12-1-1-122-1-12-122-1-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-122000000002200222200002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100220000000000-1-100
χ362222-12222-12222-122-12222-1-12-1-1-122-1-12-122-1-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-12200000000-2-20022220000-2-2-2-2111111111111-1-1-1-1-1-100-2-200000000001100
χ372222-12222-12222-122-12222-1-12-1-1-122-1-12-122-1-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2000000002200-2-2-2-200002222-1-1-1-1-1-1-1-1-1-1-1-111111100-2-200000000001100
χ382222-12222-12222-122-12222-1-12-1-1-122-1-12-122-1-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-200000000-2-200-2-2-2-20000-2-2-2-211111111111111111100220000000000-1-100
χ392-2-22222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2222-2-22-2-2-2-2-2222222-2-22-2-2222-2-22-22-2-2220022-2-222-2-200-220000-2-2220000000000000000000000000000000000000000
χ402-2-22222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2222-2-22-2-2-2-2-222222-222-222-2-22-2-22-22-2-22200-2-222-2-222002-2000022-2-20000000000000000000000000000000000000000
χ412-2-2222-12-2-2-2-22-1-211222-2-22-1-1-2-21112-1-11-11222-1-111-2-2-22-22-2-1-111-111-1-11-1-1112i−2i2-1-21-1-111002-2−i−iii-1-11100000000000000002i−2i−i−iii2i−2i0000−i−iii00000000
χ422-2-2222-12-2-2-2-22-1-211222-2-22-1-1-2-21112-1-11-11222-1-111-2-2-22-22-2-1-111-111-1-11-1-111−2i2i2-1-21-1-111002-2ii−i−i-1-1110000000000000000−2i2iii−i−i−2i2i0000ii−i−i00000000
χ432-2-2222-12-2-2-2-22-1-211222-2-22-1-1-2-21112-1-11-11222-1-111-2-2-2-22-2211-1-1-111-1-11-1-1112i−2i-212-111-1-100-22−i−iii11-1-100000000000000002i−2i−i−iii−2i2i0000ii−i−i00000000
χ442-2-2222-12-2-2-2-22-1-211222-2-22-1-1-2-21112-1-11-11222-1-111-2-2-2-22-2211-1-1-111-1-11-1-111−2i2i-212-111-1-100-22ii−i−i11-1-10000000000000000−2i2iii−i−i2i−2i0000−i−iii00000000
χ452-2-2222-1-22-2-2-22-1-2112-2-2222-1-1-2-21112-1-111-1-2-2-211-1-12222-2-2211-1-1-111-11-111-1-1002-1-21-1-11100-223−3−3311-1-10000000000000000003−3−330000003−3−3300000000
χ462-2-2222-1-22-2-2-22-1-2112-2-2222-1-1-2-21112-1-111-1-2-2-211-1-12222-2-2211-1-1-111-11-111-1-1002-1-21-1-11100-22−333−311-1-1000000000000000000−333−3000000−333−300000000
χ472-2-2222-1-22-2-2-22-1-2112-2-2222-1-1-2-21112-1-111-1-2-2-211-1-1222-222-2-1-111-111-11-111-1-100-212-111-1-1002-23−3−33-1-1110000000000000000003−3−33000000−333−300000000
χ482-2-2222-1-22-2-2-22-1-2112-2-2222-1-1-2-21112-1-111-1-2-2-211-1-1222-222-2-1-111-111-11-111-1-100-212-111-1-1002-2−333−3-1-111000000000000000000−333−30000003−3−3300000000
χ492-2-222-122-2-211-12-2-2-22-1-111-12-111-211-12-1-22-22-1-1-1-111-2112-22-222-2-2-111-12-2-1-11100-121-2-1-1112i−2i-110000-1-111−i−iii2i2i−i−i−i−i−2i−2iiiii00000000002i−2i0000−i−iii0000
χ502-2-222-122-2-211-12-2-2-22-1-111-12-111-211-12-1-22-22-1-1-1-111-2112-22-222-2-2-111-12-2-1-11100-121-2-1-111−2i2i-110000-1-111ii−i−i−2i−2iiiii2i2i−i−i−i−i0000000000−2i2i0000ii−i−i0000
χ512-2-222-122-2-211-12-2-2-22-1-111-12-111-211-12-1-22-22-1-1-1-111-211-22-22-2-222-111-12-2-1-111001-2-1211-1-12i−2i1-1000011-1-1−i−iii2i2i−i−i−i−i−2i−2iiiii0000000000−2i2i0000ii−i−i0000
χ522-2-222-122-2-211-12-2-2-22-1-111-12-111-211-12-1-22-22-1-1-1-111-211-22-22-2-222-111-12-2-1-111001-2-1211-1-1−2i2i1-1000011-1-1ii−i−i−2i−2iiiii2i2i−i−i−i−i00000000002i−2i0000−i−iii0000
χ532-2-222-12-22-211-12-2-2-2211-1-1-12-111-211-12-1-2-22-21111-1-12-1-12-2-22-2-222-111-1-2211-1-100-121-2-1-111001-1000011-1-1−i3i3i3−i300−i3−i3i3i300i3i3−i3−i30000000000000000−i3i3i3−i30000
χ542-2-222-12-22-211-12-2-2-2211-1-1-12-111-211-12-1-2-22-21111-1-12-1-12-2-22-2-222-111-1-2211-1-100-121-2-1-111001-1000011-1-1i3−i3−i3i300i3i3−i3−i300−i3−i3i3i30000000000000000i3−i3−i3i30000
χ552-2-222-12-22-211-12-2-2-2211-1-1-12-111-211-12-1-2-22-21111-1-12-1-1-222-222-2-2-111-1-2211-1-1001-2-1211-1-100-110000-1-111−i3i3i3−i300−i3−i3i3i300i3i3−i3−i30000000000000000i3−i3−i3i30000
χ562-2-222-12-22-211-12-2-2-2211-1-1-12-111-211-12-1-2-22-21111-1-12-1-1-222-222-2-2-111-1-2211-1-1001-2-1211-1-100-110000-1-111i3−i3−i3i300i3i3−i3−i300−i3−i3i3i30000000000000000−i3i3i3−i30000
χ572-2-22-1222-21-2-2221-2-2-122-2-2-1-12111-2-2-1-1212-2-1-1-122-2-211100000000-111-1-11-1-1112i−2i000000002i−2i002i2i−2i−2i00002i2i−2i−2i−i−i−i−i−i−iiiiiii−ii−i−iii002-20000000000-1100
χ582-2-22-1222-21-2-2221-2-2-122-2-2-1-12111-2-2-1-1212-2-1-1-122-2-211100000000-111-1-11-1-1112i−2i00000000−2i2i002i2i−2i−2i0000−2i−2i2i2iiiiiii−i−i−i−i−i−i−ii−i−iii00-2200000000001-100
χ592-2-22-1222-21-2-2221-2-2-122-2-2-1-12111-2-2-1-1212-2-1-1-122-2-211100000000-111-1-11-1-111−2i2i000000002i−2i00−2i−2i2i2i00002i2i−2i−2i−i−i−i−i−i−iiiiiiii−iii−i−i00-2200000000001-100
χ602-2-22-1222-21-2-2221-2-2-122-2-2-1-12111-2-2-1-1212-2-1-1-122-2-211100000000-111-1-11-1-111−2i2i00000000−2i2i00−2i−2i2i2i0000−2i−2i2i2iiiiiii−i−i−i−i−i−ii−iii−i−i002-20000000000-1100
χ6144444-2-2444-2-2-2-24-2-24-2-2-2-2-2-21-2-2-211-2-21-2-2-24-2-211114-2-24444-2-2-2-21111-2-2111100-2-2-2-2111100-2-2000011110000000000000000000000000000000000000000
χ6244444-2-2444-2-2-2-24-2-24-2-2-2-2-2-21-2-2-211-2-21-2-2-24-2-211114-2-2-4-4-4-422221111-2-21111002222-1-1-1-100220000-1-1-1-10000000000000000000000000000000000000000
χ6344444-2-2-4-44-2-2-2-24-2-242222-2-21-2-2-211-2-21-222-422-1-1-1-1-42244-4-42222111122-1-1-1-100-2-2-2-2111100220000-1-1-1-10000000000000000000000000000000000000000
χ6444444-2-2-4-44-2-2-2-24-2-242222-2-21-2-2-211-2-21-222-422-1-1-1-1-422-4-444-2-2-2-2111122-1-1-1-1002222-1-1-1-100-2-2000011110000000000000000000000000000000000000000
χ654444-244-4-4-24444-244-2-4-4-4-4-2-24-2-2-244-2-24-2-4-4222-4-4-4-422200000000-2-2-2-222222200000000000000000000000000000000000000000000000000000000000000
χ664444-24-244-2444-2-2-2-2-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-200000000111111111144000000000000-2-2-2-200000000000000000000-2-21111000000000000000000
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χ1268-8-88-4-4-4-88444-4-4444-444-4-4222-2-2-2-2-2222-24-44-2-2-2-222-42200000000-111-1-2211-1-100000000000000000000000000000000000000000000000000000000000000

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