Finite Group Databasebeta

← Group #13138994

Character table — Group #13138994

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444666666666666666666669999121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order12223446668888121224242424336666661212121224242424242424244444366612121212121224242424242424242424242444888812121212121212122424242424242424444444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ61111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ71111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ81111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ91-11-11-11-1-11ii−i−i1-1ii−i−i11-11-1-1-11-1-111iiii−i−i−i−iii−i−i1-1-11111-1-1-1iiiiii−i−i−i−i−i−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-11-11-1i−ii−ii−i1-1i−i1-1
χ101-11-11-11-1-11ii−i−i1-1ii−i−i11-11-1-1-11-1-111iiii−i−i−i−iii−i−i1-1-11111-1-1-1iiiiii−i−i−i−i−i−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-1-11-11−ii−ii−ii-11−ii-11
χ111-11-11-11-1-11ii−i−i1-1ii−i−i11-11-1-1-11-1-111iiii−i−i−i−i−i−iii1-1-11111-1-1-1iiiiii−i−i−i−i−i−i−ii-1-111−i−i−i−iiiii-1-1-1-111111-1-11i−i−iii−i1-1−ii-11
χ121-11-11-11-1-11ii−i−i1-1ii−i−i11-11-1-1-11-1-111iiii−i−i−i−i−i−iii1-1-11111-1-1-1iiiiii−i−i−i−i−i−i−ii-1-111−i−i−i−iiiii-1-1-1-11111-111-1−iii−i−ii-11i−i1-1
χ131-11-11-11-1-11−i−iii1-1−i−iii11-11-1-1-11-1-111−i−i−i−iiiiiii−i−i1-1-11111-1-1-1−i−i−i−i−i−iiiiiiii−i-1-111iiii−i−i−i−i-1-1-1-111111-1-11−iii−i−ii1-1i−i-11
χ141-11-11-11-1-11−i−iii1-1−i−iii11-11-1-1-11-1-111−i−i−i−iiiiiii−i−i1-1-11111-1-1-1−i−i−i−i−i−iiiiiiii−i-1-111iiii−i−i−i−i-1-1-1-11111-111-1i−i−iii−i-11−ii1-1
χ151-11-11-11-1-11−i−iii1-1−i−iii11-11-1-1-11-1-111−i−i−i−iiiii−i−iii1-1-11111-1-1-1−i−i−i−i−i−iiiiiii−ii11-1-1−i−i−i−iiiii1111-1-1-1-11-11-1−ii−ii−ii1-1−ii1-1
χ161-11-11-11-1-11−i−iii1-1−i−iii11-11-1-1-11-1-111−i−i−i−iiiii−i−iii1-1-11111-1-1-1−i−i−i−i−i−iiiiiii−ii11-1-1−i−i−i−iiiii1111-1-1-1-1-11-11i−ii−ii−i-11i−i-11
χ17222222222222222222222-12-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ18222222222222222222222-12-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222222222-12-1222-1-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002200220000-1-1-1-1
χ2022222222222222222222-12-1222-1-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-200-2-200001111
χ212222222222-2-2-2-222-2-2-2-22-12-1-1-122-1-1-1-1111111112222-1-1-1-12-1-12-1-1-2-21111-2-2111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-2-2-2-222-2-2-2-22-12-1-1-122-1-1-1-111111111-2-2-2-2-1-1-1-12-1-12-1-1-2-21111-2-21111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ232222222222-2-2-2-222-2-2-2-2-12-1222-1-12222-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000002200-2-2000011-1-1
χ242222222222-2-2-2-222-2-2-2-2-12-1222-1-12222-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-2-200220000-1-111
χ2522222-2-22220000-2-2000022222222-2-2-2-20000000022222222-2-2-2-2-2-2000000000000-2-2000022-2-222-2-2000000000000000000000000
χ2622222-2-22220000-2-2000022222222-2-2-2-200000000-2-2-2-22222-2-2-2-2-2-2000000000000220000-2-222-2-222000000000000000000000000
χ2722222-2-22220000-2-200002-12-1-1-122111133−3−333−3−32222-1-1-1-1-211-2110033−3−30033−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ2822222-2-22220000-2-200002-12-1-1-122111133−3−333−3−3-2-2-2-2-1-1-1-1-211-2110033−3−30033−3−322000011-1-111-1-1−3−333−3−3330000000000000000
χ2922222-2-22220000-2-200002-12-1-1-1221111−3−333−3−3332222-1-1-1-1-211-21100−3−33300−3−333-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ3022222-2-22220000-2-200002-12-1-1-1221111−3−333−3−333-2-2-2-2-1-1-1-1-211-21100−3−33300−3−33322000011-1-111-1-133−3−333−3−30000000000000000
χ3122-2-22002-2-22−22−2002−22−2222-22-2-2-200002−22−22−22−22-22-222-2-20000002−22−22−22−22−22−2002−22−22-2002-2002−22−22−22−20000000000000000
χ3222-2-22002-2-22−22−2002−22−2222-22-2-2-200002−22−22−22−2-22-2222-2-20000002−22−22−22−22−22−200−22−22-2200-2200−22−22−22−220000000000000000
χ3322-2-22002-2-22−22−2002−22−22-121-11-2-23−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232-22-2-1-11103−303−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23002−22−2-113−3-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ3422-2-22002-2-22−22−2002−22−22-121-11-2-23−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-22-22-1-11103−303−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300−22−221-1−331-1−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ3522-2-22002-2-22−22−2002−22−22-121-11-2-2−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72-22-2-1-1110−330−332−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7002−22−2-11−33-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ3622-2-22002-2-22−22−2002−22−22-121-11-2-2−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7-22-22-1-1110−330−332−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700−22−221-13−31-13−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ3722-2-22002-2-2−22−2200−22−22222-22-2-2-20000−22−22−22−222-22-222-2-2000000−22−22−22−22−22−2200−22−222-2002-200−22−22−22−220000000000000000
χ3822-2-22002-2-2−22−2200−22−22222-22-2-2-20000−22−22−22−22-22-2222-2-2000000−22−22−22−22−22−22002−22−2-2200-22002−22−22−22−20000000000000000
χ3922-2-22002-2-2−22−2200−22−222-121-11-2-23−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ232-22-2-1-11103−303−3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300−22−22-113−3-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ4022-2-22002-2-2−22−2200−22−222-121-11-2-23−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23-22-22-1-11103−303−3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23002−22−21-1−331-1−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ4122-2-22002-2-2−22−2200−22−222-121-11-2-2−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ72-22-2-1-1110−330−33−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700−22−22-11−33-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ4222-2-22002-2-2−22−2200−22−222-121-11-2-2−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7-22-22-1-1110−330−33−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7002−22−21-13−31-13−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ432-22-222-2-2-220000-22000022-22-2-2-2222-2-2000000002i2i−2i−2i2-2-22-2-2-2222000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ442-22-222-2-2-220000-22000022-22-2-2-2222-2-200000000−2i−2i2i2i2-2-22-2-2-22220000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ452-22-222-2-2-220000-2200002-1-2-111-22-1-111−i3−i3i3i3i3i3−i3−i32i2i−2i−2i-111-1-2112-1-100−i3−i3i3i300i3i3−i3−i3−2i2i0000−i−iiiii−i−i−3−33333−3−30000000000000000
χ462-22-222-2-2-220000-2200002-1-2-111-22-1-111−i3−i3i3i3i3i3−i3−i3−2i−2i2i2i-111-1-2112-1-100−i3−i3i3i300i3i3−i3−i32i−2i0000ii−i−i−i−iii33−3−3−3−3330000000000000000
χ472-22-222-2-2-220000-2200002-1-2-111-22-1-111i3i3−i3−i3−i3−i3i3i32i2i−2i−2i-111-1-2112-1-100i3i3−i3−i300−i3−i3i3i3−2i2i0000−i−iiiii−i−i33−3−3−3−3330000000000000000
χ482-22-222-2-2-220000-2200002-1-2-111-22-1-111i3i3−i3−i3−i3−i3i3i3−2i−2i2i2i-111-1-2112-1-100i3i3−i3−i300−i3−i3i3i32i−2i0000ii−i−i−i−iii−3−33333−3−30000000000000000
χ492-22-22-22-2-222i2i−2i−2i2-22i2i−2i−2i2-1-2-111-2211-1-1−i−i−i−iiiii2i2i−2i−2i-111-12-1-1-2112i2i−i−i−i−i−2i−2iiiii2i−2i22-2-2−i−i−i−iiiii-1-1-1-111110000000000000000
χ502-22-22-22-2-222i2i−2i−2i2-22i2i−2i−2i2-1-2-111-2211-1-1−i−i−i−iiiii−2i−2i2i2i-111-12-1-1-2112i2i−i−i−i−i−2i−2iiiii−2i2i-2-222iiii−i−i−i−i1111-1-1-1-10000000000000000
χ512-22-22-22-2-222i2i−2i−2i2-22i2i−2i−2i-1212-2-21-1-2-2222i2i2i2i−2i−2i−2i−2i0000-111-1-1-1-1111−i−i−i−i−i−iiiiiii0000000000000000000000002-2002i−2i0000−ii-11
χ522-22-22-22-2-222i2i−2i−2i2-22i2i−2i−2i-1212-2-21-1-2-2222i2i2i2i−2i−2i−2i−2i0000-111-1-1-1-1111−i−i−i−i−i−iiiiiii000000000000000000000000-2200−2i2i0000i−i1-1
χ532-22-22-22-2-22−2i−2i2i2i2-2−2i−2i2i2i2-1-2-111-2211-1-1iiii−i−i−i−i2i2i−2i−2i-111-12-1-1-211−2i−2iiiii2i2i−i−i−i−i2i−2i-2-222−i−i−i−iiiii1111-1-1-1-10000000000000000
χ542-22-22-22-2-22−2i−2i2i2i2-2−2i−2i2i2i2-1-2-111-2211-1-1iiii−i−i−i−i−2i−2i2i2i-111-12-1-1-211−2i−2iiiii2i2i−i−i−i−i−2i2i22-2-2iiii−i−i−i−i-1-1-1-111110000000000000000
χ552-22-22-22-2-22−2i−2i2i2i2-2−2i−2i2i2i-1212-2-21-1-2-222−2i−2i−2i−2i2i2i2i2i0000-111-1-1-1-1111iiiiii−i−i−i−i−i−i0000000000000000000000002-200−2i2i0000i−i-11
χ562-22-22-22-2-22−2i−2i2i2i2-2−2i−2i2i2i-1212-2-21-1-2-222−2i−2i−2i−2i2i2i2i2i0000-111-1-1-1-1111iiiiii−i−i−i−i−i−i000000000000000000000000-22002i−2i0000−ii1-1
χ572-2-22200-22-2−i2i2i2−i200−i2i2i2−i222-2-2-222-20000−i2i2−i2i2i2−i2i2−i22i−2i−2i2i2-22-2000000−i2i2−i2i2−i2i2i2−i2i2−i2i2−i200−222−22i−2i00−2i2i00−22−222−22−20000000000000000
χ582-2-22200-22-2−i2i2i2−i200−i2i2i2−i222-2-2-222-20000−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i2-22-2000000−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2002−2−22−2i2i002i−2i002−22−2−22−220000000000000000
χ592-2-22200-22-2−i2i2i2−i200−i2i2i2−i22-1-211-12-23−3−33ζ5+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+ζ2300−222−2−ii−i3i3i−ii3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ602-2-22200-22-2−i2i2i2−i200−i2i2i2−i22-1-211-12-23−3−33ζ5+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+ζ23002−2−22i−ii3−i3−ii−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ612-2-22200-22-2−i2i2i2−i200−i2i2i2−i22-1-211-12-2−333−3ζ13+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+ζ700−222−2−iii3−i3i−i−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ622-2-22200-22-2−i2i2i2−i200−i2i2i2−i22-1-211-12-2−333−3ζ13+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+ζ7002−2−22i−i−i3i3−iii3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.