Finite Group Databasebeta

← Group #13155002

Character table — Group #13155002

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111111122222222444444444444444444444444444444448888888812121212121212121212121212121212121212121212121212121212121212121212121218181818363636363636363636363636363636365454545454545454
order122244443666121212123333666666666666121212121212121212121212121212123666121212128888242424242424242424242424242424242424242424242424242424242424242422446688881212242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-1ii−i−i11iiii−i−i−i−i1111-1-1-1-1
χ61111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-1−i−iii11−i−i−i−iiiii-1-1-1-11111
χ71111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-111-1-1ii−i−i11iiii−i−i−i−i-1-1-1-11111
χ81111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-111-1-1−i−iii11−i−i−i−iiiii1111-1-1-1-1
χ91-1-1111-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11-1-1111-1-11-11-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-11-11-1i−ii−i1-1ii−i−iii−i−iii−i−iii−i−i
χ101-1-1111-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11-1-1111-1-11-11-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-11-11-1−ii−ii1-1−i−iii−i−iii−i−iii−i−iii
χ111-1-1111-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11-1-1111-1-1-11-11-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111111-11-11-1i−ii−i1-1ii−i−iii−i−i−i−iii−i−iii
χ121-1-1111-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11-1-1111-1-1-11-11-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111111-11-11-1−ii−ii1-1−i−iii−i−iiiii−i−iii−i−i
χ131-1-11-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111-1-11-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-111-1-111-1-111-111-1-1-1-111−i−iiiii−i−i
χ141-1-11-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111-1-11-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-111-1-11-111-11-1-1-11111-1-1ii−i−i−i−iii
χ151-1-11-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111-1-11-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-111-1-111-1-111-111-1-1-1-111ii−i−i−i−iii
χ161-1-11-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111-1-11-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-111-1-11-111-11-1-1-11111-1-1−i−iiiii−i−i
χ1722222222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-2-2-20000-2-20000000000000000
χ1822222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-2-2-2110000110000000000000000
χ1922222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-2-2-2110000110000000000000000
χ2022222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-10000-1-10000000000000000
χ2122222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-21111-2-211112222-1-10000-1-10000000000000000
χ222222-2-2-2-22222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000022-2-2220000-2-20000000000000000
χ232222-2-2-2-2-1-1-1-1111122-1-12222-1-1-1-122-1-1-2-2-2-21111-2-21111-2-2-1-1-1-1111100003−33−3−33−330033−3−30033−3−300−3−33300−3−33322-2-2-1-10000110000000000000000
χ242222-2-2-2-2-1-1-1-1111122-1-12222-1-1-1-122-1-1-2-2-2-21111-2-21111-2-2-1-1-1-111110000−33−333−33−300−3−33300−3−3330033−3−30033−3−322-2-2-1-10000110000000000000000
χ252222-2-2-2-2-1-1-1-1111122-1-12222-1-1-1-122-1-1-2-2-2-21111-2-21111-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii-2-222110000-1-10000000000000000
χ262222-2-2-2-2-1-1-1-1111122-1-12222-1-1-1-122-1-1-2-2-2-21111-2-21111-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i-2-222110000-1-10000000000000000
χ2722-2-22i−2i2i−2i22-2-22i−2i2i−2i222222-2-222-2-2-2-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000002−22−2−i2i2−i2i2
χ2822-2-22i−2i2i−2i22-2-22i−2i2i−2i222222-2-222-2-2-2-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i−2i22-2-22i−2i2i−2i00000000000000000000000000000000000000000000000000000000−22−22i2−i2i2−i2
χ2922-2-2−2i2i−2i2i22-2-2−2i2i−2i2i222222-2-222-2-2-2-2-2-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i2i22-2-2−2i2i−2i2i000000000000000000000000000000000000000000000000000000002−22−2i2−i2i2−i2
χ3022-2-2−2i2i−2i2i22-2-2−2i2i−2i2i222222-2-222-2-2-2-2-2-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i2i22-2-2−2i2i−2i2i00000000000000000000000000000000000000000000000000000000−22−22−i2i2−i2i2
χ312-22-22i−2i−2i2i2-22-2−2i2i2i−2i2222-2-222-2-222-2-2-2-22i−2i−2i2i−2i−2i2i2i2i−2i2i2i−2i−2i−2i2i2-22-22i−2i−2i2i00000000000000000000000000000000000000000000000000000000−i2i2i2−i2−222−2
χ322-22-22i−2i−2i2i2-22-2−2i2i2i−2i2222-2-222-2-222-2-2-2-22i−2i−2i2i−2i−2i2i2i2i−2i2i2i−2i−2i−2i2i2-22-22i−2i−2i2i00000000000000000000000000000000000000000000000000000000i2−i2−i2i22−2−22
χ332-22-2−2i2i2i−2i2-22-22i−2i−2i2i2222-2-222-2-222-2-2-2-2−2i2i2i−2i2i2i−2i−2i−2i2i−2i−2i2i2i2i−2i2-22-2−2i2i2i−2i00000000000000000000000000000000000000000000000000000000−i2i2i2−i22−2−22
χ342-22-2−2i2i2i−2i2-22-22i−2i−2i2i2222-2-222-2-222-2-2-2-2−2i2i2i−2i2i2i−2i−2i−2i2i−2i−2i2i2i2i−2i2-22-2−2i2i2i−2i00000000000000000000000000000000000000000000000000000000i2−i2−i2i2−222−2
χ352-2-2222-2-22-2-22-2-2222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2222222-2-22-2-2222-2-2000000000000000000000000000000000000-22-22-220000-220000000000000000
χ362-2-2222-2-2-111-111-1-122-1-1-2-2-2-2111122-1-122-2-2111122-1-1-1-1-2-2-111-1-1-1110000−i3i3i3−i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i3-22-221-100001-10000000000000000
χ372-2-2222-2-2-111-111-1-122-1-1-2-2-2-2111122-1-122-2-2111122-1-1-1-1-2-2-111-1-1-1110000i3−i3−i3i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i3-22-221-100001-10000000000000000
χ382-2-2222-2-2-111-111-1-122-1-1-2-2-2-2111122-1-122-2-2111122-1-1-1-1-2-2-111-1-1-1112-22-2-1-111-1-11122-1-1-1-1-2-2111122-1-1-1-1-2-211112-22-2-110000-110000000000000000
χ392-2-2222-2-2-111-111-1-122-1-1-2-2-2-2111122-1-122-2-2111122-1-1-1-1-2-2-111-1-1-111-22-2211-1-111-1-1-2-2111122-1-1-1-1-2-2111122-1-1-1-12-22-2-110000-110000000000000000
χ402-2-22-2-2222-2-2222-2-22222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2222-2-22-2-2220000000000000000000000000000000000002-2-222-20000-220000000000000000
χ412-2-22-2-222-111-1-1-11122-1-1-2-2-2-2111122-1-1-2-222-1-1-1-1-2-2111122-111-111-1-100003−3−33−333−30033−3−300−3−33300−3−3330033−3−32-2-22-1100001-10000000000000000
χ422-2-22-2-222-111-1-1-11122-1-1-2-2-2-2111122-1-1-2-222-1-1-1-1-2-2111122-111-111-1-10000−333−33−3−3300−3−3330033−3−30033−3−300−3−3332-2-22-1100001-10000000000000000
χ432-2-22-2-222-111-1-1-11122-1-1-2-2-2-2111122-1-1-2-222-1-1-1-1-2-2111122-111-111-1-12i−2i−2i2i−i−iiiii−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-222-21-10000-110000000000000000
χ442-2-22-2-222-111-1-1-11122-1-1-2-2-2-2111122-1-1-2-222-1-1-1-1-2-2111122-111-111-1-1−2i2i2i−2iii−i−i−i−iii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-222-21-10000-110000000000000000
χ4544444444444444441-2111-21-211111-211-2-2111111111111-2-2-2-2-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ4644444444444444441-2111-21-211111-211-2-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111111111110000000000000000000000000000
χ474444444444444444-21-2-2-21-21-2-2-2-2-21-2-211-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000000000222200-1-1-1-1-1-1-1-100000000
χ484444444444444444-21-2-2-21-21-2-2-2-2-21-2-211-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000000000-2-2-2-2001111111100000000
χ4944444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i321-2−1−3i32−1+3i32-2-211−1−3i32−1+3i32−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000000000000000000
χ5044444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i321-2−1−3i32−1+3i32-2-211−1−3i32−1+3i32−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-211111111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000000000000000000
χ5144444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i321-2−1+3i32−1−3i32-2-211−1+3i32−1−3i32−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-2111111112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000000000000000000000
χ5244444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i321-2−1+3i32−1−3i32-2-211−1+3i32−1−3i32−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-211111111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000000000000000000000
χ534444-4-4-4-44444-4-4-4-41-2111-21-211111-21122-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii0000000000000000000000000000
χ544444-4-4-4-44444-4-4-4-41-2111-21-211111-21122-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22222−2i−2i2i2i−2i−2i−2i−2i2i2i2i2iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i0000000000000000000000000000
χ554444-4-4-4-44444-4-4-4-4-21-2-2-21-21-2-2-2-2-21-2-2-1-1222222222222-1-11111-1-1-1-10000000000000000000000000000000000000000002i2i−2i−2i00−i−i−i−iiiii00000000
χ564444-4-4-4-44444-4-4-4-4-21-2-2-21-21-2-2-2-2-21-2-2-1-1222222222222-1-11111-1-1-1-1000000000000000000000000000000000000000000−2i−2i2i2i00iiii−i−i−i−i00000000
χ574444-4-4-4-4-2-2-2-222221-2−1−3i32−1+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i321-2−1−3i32−1+3i3222-1-11+3i321−3i321+3i321−3i32-1-11+3i321−3i321+3i321−3i32221111-1-1-1-12i2i−2i−2i2ζ222ζ142ζ222ζ14−2ζ22−2ζ14−2ζ22−2ζ14−i−i−ζ22−ζ22−ζ14−ζ14−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ14iiζ22ζ22ζ14ζ140000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.