Finite Group Databasebeta

← Group #13139065

Character table — Group #13139065

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444666666666666666666669999121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order12223446668888121224242424336666661212121224242424242424244444366612121212121224242424242424242424242422666688881212121224242424242424242244444466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1
χ61111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ71111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-11111-1-1-1-1
χ81111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-11111
χ91-1-1111-1-1-11ii−i−i1-1ii−i−i11-1-1-111-111-1-1iiii−i−i−i−i11-1-11-1-11111-1-1-1iiiiii−i−i−i−i−i−i1-111-1-1ii−i−i11-1-1iiii−i−i−i−i1-1i−ii−i1-11-1i−i1-1i−i
χ101-1-1111-1-1-11ii−i−i1-1ii−i−i11-1-1-111-111-1-1iiii−i−i−i−i11-1-11-1-11111-1-1-1iiiiii−i−i−i−i−i−i1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-11−ii−ii-11-11−ii-11−ii
χ111-1-1111-1-1-11ii−i−i1-1ii−i−i11-1-1-111-111-1-1iiii−i−i−i−i-1-1111-1-11111-1-1-1iiiiii−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiii1-1i−i−ii-111-1−ii-11i−i
χ121-1-1111-1-1-11ii−i−i1-1ii−i−i11-1-1-111-111-1-1iiii−i−i−i−i-1-1111-1-11111-1-1-1iiiiii−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiii-11−iii−i1-1-11i−i1-1−ii
χ131-1-1111-1-1-11−i−iii1-1−i−iii11-1-1-111-111-1-1−i−i−i−iiiii11-1-11-1-11111-1-1-1−i−i−i−i−i−iiiiiii1-111-1-1−i−iii11-1-1−i−i−i−iiiii1-1−ii−ii1-11-1−ii1-1−ii
χ141-1-1111-1-1-11−i−iii1-1−i−iii11-1-1-111-111-1-1−i−i−i−iiiii11-1-11-1-11111-1-1-1−i−i−i−i−i−iiiiiii1-111-1-1−i−iii11-1-1−i−i−i−iiiii-11i−ii−i-11-11i−i-11i−i
χ151-1-1111-1-1-11−i−iii1-1−i−iii11-1-1-111-111-1-1−i−i−i−iiiii-1-1111-1-11111-1-1-1−i−i−i−i−i−iiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−i1-1−iii−i-111-1i−i-11−ii
χ161-1-1111-1-1-11−i−iii1-1−i−iii11-1-1-111-111-1-1−i−i−i−iiiii-1-1111-1-11111-1-1-1−i−i−i−i−i−iiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−i-11i−i−ii1-1-11−ii1-1i−i
χ17222222222222222222222-122-1-12-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000022220000-1-10000-1-1
χ18222222222222222222222-122-1-12-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000-2-2-2-2000011000011
χ1922222222222222222222-12-1-122-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2022222222222222222222-12-1-122-12-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1-2-21111-2-2-2-21111111111110000000000000000
χ212222222222-2-2-2-222-2-2-2-22-122-1-12-12222-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000022-2-20000-1-1000011
χ222222222222-2-2-2-222-2-2-2-22-122-1-12-12222-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000-2-2220000110000-1-1
χ232222222222-2-2-2-222-2-2-2-2-12-1-122-12-1-1-1-1111111112222-1-1-1-12-1-12-1-1-2-21111-2-2111122-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ242222222222-2-2-2-222-2-2-2-2-12-1-122-12-1-1-1-111111111-2-2-2-2-1-1-1-12-1-12-1-1-2-21111-2-21111-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ2522222-2-22220000-2-2000022222222-2-2-2-20000000022222222-2-2-2-2-2-2000000000000-2-2-2-2-2-200002222000000000000000000000000
χ2622222-2-22220000-2-2000022222222-2-2-2-200000000-2-2-2-22222-2-2-2-2-2-20000000000002222220000-2-2-2-2000000000000000000000000
χ2722222-2-22220000-2-20000-12-1-122-12111133−3−333−3−32222-1-1-1-1-211-2110033−3−30033−3−3-2-211110000-1-1-1-133−3−333−3−30000000000000000
χ2822222-2-22220000-2-20000-12-1-122-12111133−3−333−3−3-2-2-2-2-1-1-1-1-211-2110033−3−30033−3−322-1-1-1-100001111−3−333−3−3330000000000000000
χ2922222-2-22220000-2-20000-12-1-122-121111−3−333−3−3332222-1-1-1-1-211-21100−3−33300−3−333-2-211110000-1-1-1-1−3−333−3−3330000000000000000
χ3022222-2-22220000-2-20000-12-1-122-121111−3−333−3−333-2-2-2-2-1-1-1-1-211-21100−3−33300−3−33322-1-1-1-10000111133−3−333−3−30000000000000000
χ3122-2-22002-2-22−22−2002−22−2222-2-2-2-2200002−22−22−22−22i−2i2i−2i22-2-20000002−22−22−22−22−22−2000000−i2i2−i2i22i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-2-22002-2-22−22−2002−22−2222-2-2-2-2200002−22−22−22−2−2i2i−2i2i22-2-20000002−22−22−22−22−22−2000000i2−i2i2−i2−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-2-22002-2-22−22−2002−22−2-12-11-2-2123−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232i−2i2i−2i-1-11103−303−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300−i3i3−i3i3−i2i2−i2i2−ii−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ3422-2-22002-2-22−22−2002−22−2-12-11-2-2123−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−2i2i−2i2i-1-11103−303−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300i3−i3i3−i3i2−i2i2−i2i−ii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ3522-2-22002-2-22−22−2002−22−2-12-11-2-212−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72i−2i2i−2i-1-1110−330−332−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700i3−i3i3−i3−i2i2−i2i2−ii−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ3622-2-22002-2-22−22−2002−22−2-12-11-2-212−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−2i2i−2i2i-1-1110−330−332−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700−i3i3−i3i3i2−i2i2−i2i−ii−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ3722-2-22002-2-2−22−2200−22−22222-2-2-2-220000−22−22−22−222i−2i2i−2i22-2-2000000−22−22−22−22−22−22000000i2−i2i2−i22i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-2-22002-2-2−22−2200−22−22222-2-2-2-220000−22−22−22−22−2i2i−2i2i22-2-2000000−22−22−22−22−22−22000000−i2i2−i2i2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-2-22002-2-2−22−2200−22−22-12-11-2-2123−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ232i−2i2i−2i-1-11103−303−3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300−i3i3−i3i3i2−i2i2−i2−ii−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ4022-2-22002-2-2−22−2200−22−22-12-11-2-2123−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2i2i−2i2i-1-11103−303−3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300i3−i3i3−i3−i2i2−i2i2i−ii−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ4122-2-22002-2-2−22−2200−22−22-12-11-2-212−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ72i−2i2i−2i-1-1110−330−33−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700i3−i3i3−i3i2−i2i2−i2−ii−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ4222-2-22002-2-2−22−2200−22−22-12-11-2-212−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2i2i−2i2i-1-1110−330−33−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700−i3i3−i3i3−i2i2−i2i2i−ii−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ432-22-2200-22-2−i2i2i2−i200−i2i2i2−i222-222-2-2-20000−i2i2−i2i2i2−i2i2−i22i−2i−2i2i2-22-2000000−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2000000−222−22i−2i−2i2i−22−222−22−20000000000000000
χ442-22-2200-22-2−i2i2i2−i200−i2i2i2−i222-222-2-2-20000−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i2-22-2000000−i2i2−i2i2−i2i2i2−i2i2−i2i2−i20000002−2−22−2i2i2i−2i2−22−2−22−220000000000000000
χ452-22-2200-22-2−i2i2i2−i200−i2i2i2−i2-121-12-21-23−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ72i−2i−2i2i-11-1103−30−33−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700−i3i3i3−i3−222−2−iii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ462-22-2200-22-2−i2i2i2−i200−i2i2i2−i2-121-12-21-23−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−2i2i2i−2i-11-1103−30−33−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700i3−i3−i3i32−2−22i−i−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ472-22-2200-22-2−i2i2i2−i200−i2i2i2−i2-121-12-21-2−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ232i−2i−2i2i-11-110−3303−3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300i3−i3−i3i3−222−2−iii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ482-22-2200-22-2−i2i2i2−i200−i2i2i2−i2-121-12-21-2−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−2i2i2i−2i-11-110−3303−3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300−i3i3i3−i32−2−22i−i−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ492-22-2200-22-2i2−i2−i2i200i2−i2−i2i222-222-2-2-20000i2−i2i2−i2−i2i2−i2i22i−2i−2i2i2-22-2000000i2−i2i2−i2i2−i2−i2i2−i2i2−i2i20000002−2−222i−2i−2i2i2−22−2−22−220000000000000000
χ502-22-2200-22-2i2−i2−i2i200i2−i2−i2i222-222-2-2-20000i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i2-22-2000000i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2000000−222−2−2i2i2i−2i−22−222−22−20000000000000000
χ512-22-2200-22-2i2−i2−i2i200i2−i2−i2i2-121-12-21-23−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ72i−2i−2i2i-11-1103−30−33i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700−i3i3i3−i32−2−22−iii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ522-22-2200-22-2i2−i2−i2i200i2−i2−i2i2-121-12-21-23−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−2i2i2i−2i-11-1103−30−33i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700i3−i3−i3i3−222−2i−i−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ532-22-2200-22-2i2−i2−i2i200i2−i2−i2i2-121-12-21-2−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ232i−2i−2i2i-11-110−3303−3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300i3−i3−i3i32−2−22−iii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ542-22-2200-22-2i2−i2−i2i200i2−i2−i2i2-121-12-21-2−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−2i2i2i−2i-11-110−3303−3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300−i3i3i3−i3−222−2i−i−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ552-2-2222-2-2-222i2i−2i−2i2-22i2i−2i−2i2-1-2-21-12122-2-22i2i2i2i−2i−2i−2i−2i0000-111-1-1-1-1111−i−i−i−i−i−iiiiiii00000000000000000000002-22i−2i0000-110000−ii
χ562-2-2222-2-2-222i2i−2i−2i2-22i2i−2i−2i2-1-2-21-12122-2-22i2i2i2i−2i−2i−2i−2i0000-111-1-1-1-1111−i−i−i−i−i−iiiiiii0000000000000000000000-22−2i2i00001-10000i−i
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.