Finite Group Databasebeta

← Group #13155423

Character table — Group #13155423

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122222222222222444444444466666666666612121212121236362222444444444444448888888888121212121212121212121212242424242424727233336666666666666612121212121212121212181818181818181818181818363636363636108108
order1244233466661212121212123666612121212124444121212121212121288242424242436121263312666612121212121236666121212121212121212121212121212121224242424242461222442664666612121212121266666121212121244441212121212121212882424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1ii−i−iiiii−i−i−i−ii−iii−i−i1-111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1ii−i−iiiii−i−i−i−ii−iii−i−i1-111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1ii−i−iiiii−i−i−i−ii−iii−i−i1-1
χ611-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1ii−i−iiiii−i−i−i−i−ii−i−iii-1111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1ii−i−iiiii−i−i−i−i−ii−i−iii-1111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1ii−i−iiiii−i−i−i−i−ii−i−iii-11
χ711-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1−i−iii−i−i−i−iiiiii−iii−i−i-1111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1−i−iii−i−i−i−iiiiii−iii−i−i-1111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1−i−iii−i−i−i−iiiiii−iii−i−i-11
χ811-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1−i−iii−i−i−i−iiiii−ii−i−iii1-111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1−i−iii−i−i−i−iiiii−ii−i−iii1-111-1-1-111111-1-111-1-1-1-11-1-1-11111-1-1−i−iii−i−i−i−iiiii−ii−i−iii1-1
χ9222222-122-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100222222-122-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100222222-122-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100
χ10222222-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2111100222222-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2111100222222-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2111100
χ1122222-122-12-1-1-1-1-1-122-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-10000000022222-122-12-1-1-1-1-1-122-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-10000000022222-122-12-1-1-1-1-1-122-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ1222222-122-12-1-1-1-1-1-122-12-1-1-12-1-1-1-1-2-2-2-2111111110000000022222-122-12-1-1-1-1-1-122-12-1-1-12-1-1-1-1-2-2-2-2111111110000000022222-122-12-1-1-1-1-1-122-12-1-1-12-1-1-1-1-2-2-2-21111111100000000
χ132222-222-222-2-2-2-222222-2-2-22-2-2-222000000000000000000002222-222-222-2-2-2-222222-2-2-22-2-2-222000000000000000000002222-222-222-2-2-2-222222-2-2-22-2-2-22200000000000000000000
χ142222-22-1-22-1-2-2-2-222-1-1-1111-1111-1-100000000000000−i3i3−i3i3002222-22-1-22-1-2-2-2-222-1-1-1111-1111-1-100000000000000−i3i3−i3i3002222-22-1-22-1-2-2-2-222-1-1-1111-1111-1-100000000000000−i3i3−i3i300
χ152222-22-1-22-1-2-2-2-222-1-1-1111-1111-1-100000000000000i3−i3i3−i3002222-22-1-22-1-2-2-2-222-1-1-1111-1111-1-100000000000000i3−i3i3−i3002222-22-1-22-1-2-2-2-222-1-1-1111-1111-1-100000000000000i3−i3i3−i300
χ162222-2-12-2-121111-1-122-1-211-1-211-1-1000033−3−333−3−3000000002222-2-12-2-121111-1-122-1-211-1-211-1-1000033−3−333−3−3000000002222-2-12-2-121111-1-122-1-211-1-211-1-1000033−3−333−3−300000000
χ172222-2-12-2-121111-1-122-1-211-1-211-1-10000−3−333−3−333000000002222-2-12-2-121111-1-122-1-211-1-211-1-10000−3−333−3−333000000002222-2-12-2-121111-1-122-1-211-1-211-1-10000−3−333−3−33300000000
χ1822-2-2222-22222-2-2-2-2-2-222222-2-2-2-2-20000000000000000000022-2-2222-22222-2-2-2-2-2-222222-2-2-2-2-20000000000000000000022-2-2222-22222-2-2-2-2-2-222222-2-2-2-2-200000000000000000000
χ1922-2-222-1-22-122-2-2-2-211-1-1-1-1-111111000000000000003−3−330022-2-222-1-22-122-2-2-2-211-1-1-1-1-111111000000000000003−3−330022-2-222-1-22-122-2-2-2-211-1-1-1-1-111111000000000000003−3−3300
χ2022-2-222-1-22-122-2-2-2-211-1-1-1-1-11111100000000000000−333−30022-2-222-1-22-122-2-2-2-211-1-1-1-1-11111100000000000000−333−30022-2-222-1-22-122-2-2-2-211-1-1-1-1-11111100000000000000−333−300
χ2122-2-22-12-2-12-1-11111-2-2-12-1-1-1-211110000−i3−i3i3i3i3i3−i3−i30000000022-2-22-12-2-12-1-11111-2-2-12-1-1-1-211110000−i3−i3i3i3i3i3−i3−i30000000022-2-22-12-2-12-1-11111-2-2-12-1-1-1-211110000−i3−i3i3i3i3i3−i3−i300000000
χ2222-2-22-12-2-12-1-11111-2-2-12-1-1-1-211110000i3i3−i3−i3−i3−i3i3i30000000022-2-22-12-2-12-1-11111-2-2-12-1-1-1-211110000i3i3−i3−i3−i3−i3i3i30000000022-2-22-12-2-12-1-11111-2-2-12-1-1-1-211110000i3i3−i3−i3−i3−i3i3i300000000
χ2322-2-2-22-122-1-2-222-2-211-1111-1-1-1-1110000000000002i−2i−i−iii0022-2-2-22-122-1-2-222-2-211-1111-1-1-1-1110000000000002i−2i−i−iii0022-2-2-22-122-1-2-222-2-211-1111-1-1-1-1110000000000002i−2i−i−iii00
χ2422-2-2-22-122-1-2-222-2-211-1111-1-1-1-111000000000000−2i2iii−i−i0022-2-2-22-122-1-2-222-2-211-1111-1-1-1-111000000000000−2i2iii−i−i0022-2-2-22-122-1-2-222-2-211-1111-1-1-1-111000000000000−2i2iii−i−i00
χ2522-2-2-2-122-1211-1-111-2-2-1-211-12-1-1112i2i−2i−2i−i−i−i−iiiii0000000022-2-2-2-122-1211-1-111-2-2-1-211-12-1-1112i2i−2i−2i−i−i−i−iiiii0000000022-2-2-2-122-1211-1-111-2-2-1-211-12-1-1112i2i−2i−2i−i−i−i−iiiii00000000
χ2622-2-2-2-122-1211-1-111-2-2-1-211-12-1-111−2i−2i2i2iiiii−i−i−i−i0000000022-2-2-2-122-1211-1-111-2-2-1-211-12-1-111−2i−2i2i2iiiii−i−i−i−i0000000022-2-2-2-122-1211-1-111-2-2-1-211-12-1-111−2i−2i2i2iiiii−i−i−i−i00000000
χ272-22i−2i0220-2-200002i−2i2i−2i2000-20002i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002-22i−2i0220-2-200002i−2i2i−2i2000-20002i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002-22i−2i0220-2-200002i−2i2i−2i2000-20002i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ282-22i−2i0220-2-200002i−2i2i−2i2000-20002i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002-22i−2i0220-2-200002i−2i2i−2i2000-20002i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002-22i−2i0220-2-200002i−2i2i−2i2000-20002i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ292-22i−2i0-1201-2−i3i33−3−ii2i−2i-10−i3i3103−3−ii1+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000002-22i−2i0-1201-2−i3i33−3−ii2i−2i-10−i3i3103−3−ii1+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000002-22i−2i0-1201-2−i3i33−3−ii2i−2i-10−i3i3103−3−ii1+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ302-22i−2i0-1201-2−i3i33−3−ii2i−2i-10−i3i3103−3−ii−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000002-22i−2i0-1201-2−i3i33−3−ii2i−2i-10−i3i3103−3−ii−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000002-22i−2i0-1201-2−i3i33−3−ii2i−2i-10−i3i3103−3−ii−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ312-22i−2i0-1201-2i3−i3−33−ii2i−2i-10i3−i310−33−ii1+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000002-22i−2i0-1201-2i3−i3−33−ii2i−2i-10i3−i310−33−ii1+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000002-22i−2i0-1201-2i3−i3−33−ii2i−2i-10i3−i310−33−ii1+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ322-22i−2i0-1201-2i3−i3−33−ii2i−2i-10i3−i310−33−ii−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000002-22i−2i0-1201-2i3−i3−33−ii2i−2i-10i3−i310−33−ii−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000002-22i−2i0-1201-2i3−i3−33−ii2i−2i-10i3−i310−33−ii−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ332-2−2i2i0220-2-20000−2i2i−2i2i2000-2000−2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002-2−2i2i0220-2-20000−2i2i−2i2i2000-2000−2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002-2−2i2i0220-2-20000−2i2i−2i2i2000-2000−2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ342-2−2i2i0220-2-20000−2i2i−2i2i2000-2000−2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002-2−2i2i0220-2-20000−2i2i−2i2i2000-2000−2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002-2−2i2i0220-2-20000−2i2i−2i2i2000-2000−2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ352-2−2i2i0-1201-2−i3i3−33i−i−2i2i-10−i3i310−33i−i1−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000002-2−2i2i0-1201-2−i3i3−33i−i−2i2i-10−i3i310−33i−i1−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000002-2−2i2i0-1201-2−i3i3−33i−i−2i2i-10−i3i310−33i−i1−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ362-2−2i2i0-1201-2−i3i3−33i−i−2i2i-10−i3i310−33i−i−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000002-2−2i2i0-1201-2−i3i3−33i−i−2i2i-10−i3i310−33i−i−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000002-2−2i2i0-1201-2−i3i3−33i−i−2i2i-10−i3i310−33i−i−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ372-2−2i2i0-1201-2i3−i33−3i−i−2i2i-10i3−i3103−3i−i1−i−1+i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000002-2−2i2i0-1201-2i3−i33−3i−i−2i2i-10i3−i3103−3i−i1−i−1+i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000002-2−2i2i0-1201-2i3−i33−3i−i−2i2i-10i3−i3103−3i−i1−i−1+i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ382-2−2i2i0-1201-2i3−i33−3i−i−2i2i-10i3−i3103−3i−i−1+i1−i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000002-2−2i2i0-1201-2i3−i33−3i−i−2i2i-10i3−i3103−3i−i−1+i1−i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000002-2−2i2i0-1201-2i3−i33−3i−i−2i2i-10i3−i3103−3i−i−1+i1−i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ3944444-2-24-2-2-2-2-2-2-2-2-2-21-2111-211110000000000000000000044444-2-24-2-2-2-2-2-2-2-2-2-21-2111-211110000000000000000000044444-2-24-2-2-2-2-2-2-2-2-2-21-2111-2111100000000000000000000
χ404444-4-2-2-4-2-22222-2-2-2-212-1-112-1-111000000000000000000004444-4-2-2-4-2-22222-2-2-2-212-1-112-1-111000000000000000000004444-4-2-2-4-2-22222-2-2-2-212-1-112-1-11100000000000000000000
χ4144-4-44-2-2-4-2-2-2-22222221-21112-1-1-1-10000000000000000000044-4-44-2-2-4-2-2-2-22222221-21112-1-1-1-10000000000000000000044-4-44-2-2-4-2-2-2-22222221-21112-1-1-1-100000000000000000000
χ4244-4-4-4-2-24-2-222-2-2222212-1-11-211-1-10000000000000000000044-4-4-4-2-24-2-222-2-2222212-1-11-211-1-10000000000000000000044-4-4-4-2-24-2-222-2-2222212-1-11-211-1-100000000000000000000
χ434-44i−4i04-20-4200004i−4i−2i2i-20002000−2i2i000000000000000000004-44i−4i04-20-4200004i−4i−2i2i-20002000−2i2i000000000000000000004-44i−4i04-20-4200004i−4i−2i2i-20002000−2i2i00000000000000000000
χ444-44i−4i0-2-2022−2i32i323−23−2i2i−2i2i10i3−i3-10−33i−i000000000000000000004-44i−4i0-2-2022−2i32i323−23−2i2i−2i2i10i3−i3-10−33i−i000000000000000000004-44i−4i0-2-2022−2i32i323−23−2i2i−2i2i10i3−i3-10−33i−i00000000000000000000
χ454-44i−4i0-2-20222i3−2i3−2323−2i2i−2i2i10−i3i3-103−3i−i000000000000000000004-44i−4i0-2-20222i3−2i3−2323−2i2i−2i2i10−i3i3-103−3i−i000000000000000000004-44i−4i0-2-20222i3−2i3−2323−2i2i−2i2i10−i3i3-103−3i−i00000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.