Finite Group Databasebeta

← Group #11785849

Character table — Group #11785849

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size111111112222222222222222222244444444444444448888888888888888888888121212121212121212121212121212121212121212121212121212121212121218181818242424242424242436367272
order1222444422334466666612121212121212123666666612121212121212126688121224242424242424242424242424242424444444444444444412121212121212121212121212121212224412121212121212122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ61111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111-1-1
χ91111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1-11i−i
χ101111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1-1111-1−ii
χ111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1i−i11iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-11111-1-11-1−ii
χ121111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-111-11i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1-11−ii
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1-1111-1i−i
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-11111-1-11-1i−i
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1−ii11−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-111-11−ii
χ1722222222222-1222-122-1-122-1-122-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1000022220000222200000000-1-1-1-1-1-1-1-100000000-1-1-1-10000
χ1822222222222-1222-122-1-122-1-122-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000-2-2-2-200000000111111110000000011110000
χ1922222222222-1222-122-1-122-1-122-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2-1-1-2-211-2-21111111111000022220000-2-2-2-2000000001111111100000000-1-1-1-10000
χ2022222222222-1222-122-1-122-1-122-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2-1-1-2-211-2-211111111110000-2-2-2-20000222200000000-1-1-1-1-1-1-1-10000000011110000
χ212222222222-1222-12-1-122-1-122-1-122-1-12-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-12222000022220000-1-1-1-1-1-1-1-1000000000000-1-1-1-100000000
χ222222222222-1222-12-1-122-1-122-1-122-1-12-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-2000011111111000000000000111100000000
χ232222222222-1222-12-1-122-1-122-1-122-1-12-1-1-1-12-1-122-1-1-1-1-1-1-2-2-1-111-2-211-2-21111111122220000-2-2-2-2000011111111000000000000-1-1-1-100000000
χ242222222222-1222-12-1-122-1-122-1-122-1-12-1-1-1-12-1-122-1-1-1-1-1-1-2-2-1-111-2-211-2-211111111-2-2-2-2000022220000-1-1-1-1-1-1-1-1000000000000111100000000
χ2522222222-2-222-2-2222222222222222-2-2222-2-2-2-2-2-22222-2-200-2-2000000000000000000000000000000000000000000000000222200000000-2-200
χ2622222222-2-222-2-2222222222222222-2-2222-2-2-2-2-2-22222-2-200-2-2000000000000000000000000000000000000000000000000-2-2-2-2000000002200
χ272222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22200-2-200000000000000000000000000000000000000000000000022-2-2000000002-200
χ282222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22200-2-2000000000000000000000000000000000000000000000000-2-22200000000-2200
χ292222-2-2-2-2-2-22-1222-122-1-1-2-211-2-211-1-21-1-1-1-2122-1-11111112i−2i-1-12i2i−i−i−2i−2iii−i−i−i−iiiii000022-2-200002i2i−2i−2i00000000−i−i−i−iiiii00000000-1-1110000
χ302222-2-2-2-2-2-22-1222-122-1-1-2-211-2-211-1-21-1-1-1-2122-1-11111112i−2i-1-12i2i−i−i−2i−2iii−i−i−i−iiiii0000-2-2220000−2i−2i2i2i00000000iiii−i−i−i−i0000000011-1-10000
χ312222-2-2-2-2-2-22-1222-122-1-1-2-211-2-211-1-21-1-1-1-2122-1-1111111−2i2i-1-1−2i−2iii2i2i−i−iiiii−i−i−i−i000022-2-20000−2i−2i2i2i00000000iiii−i−i−i−i00000000-1-1110000
χ322222-2-2-2-2-2-22-1222-122-1-1-2-211-2-211-1-21-1-1-1-2122-1-1111111−2i2i-1-1−2i−2iii2i2i−i−iiiii−i−i−i−i0000-2-22200002i2i−2i−2i00000000−i−i−i−iiiii0000000011-1-10000
χ332222-2-2-2-2-2-2-1222-12-1-12211-2-211-2-2-11-2-1-1-11-2-1-1221111112i−2i-1-1−i−i2i2iii−2i−2i−i−i−i−iiiii22-2-200002i2i−2i−2i0000−i−i−i−iiiii000000000000-1-11100000000
χ342222-2-2-2-2-2-2-1222-12-1-12211-2-211-2-2-11-2-1-1-11-2-1-1221111112i−2i-1-1−i−i2i2iii−2i−2i−i−i−i−iiiii-2-2220000−2i−2i2i2i0000iiii−i−i−i−i00000000000011-1-100000000
χ352222-2-2-2-2-2-2-1222-12-1-12211-2-211-2-2-11-2-1-1-11-2-1-122111111−2i2i-1-1ii−2i−2i−i−i2i2iiiii−i−i−i−i22-2-20000−2i−2i2i2i0000iiii−i−i−i−i000000000000-1-11100000000
χ362222-2-2-2-2-2-2-1222-12-1-12211-2-211-2-2-11-2-1-1-11-2-1-122111111−2i2i-1-1ii−2i−2i−i−i2i2iiiii−i−i−i−i-2-22200002i2i−2i−2i0000−i−i−i−iiiii00000000000011-1-100000000
χ3722-2-22i−2i2i−2i002200-2-22-22-22i−2i2i−2i2i−2i2i−2i2002-2-20000002i−2i2i−2i0000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i000000000000
χ3822-2-22i−2i2i−2i002200-2-22-22-22i−2i2i−2i2i−2i2i−2i2002-2-20000002i−2i2i−2i0000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i000000000000
χ3922-2-22i−2i2i−2i002200-2-22-22-22i−2i2i−2i2i−2i2i−2i2002-2-20000002i−2i2i−2i000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i000000000000
χ4022-2-22i−2i2i−2i002200-2-22-22-22i−2i2i−2i2i−2i2i−2i2002-2-20000002i−2i2i−2i000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i000000000000
χ4122-2-2−2i2i−2i2i002200-2-22-22-2−2i2i−2i2i−2i2i−2i2i2002-2-2000000−2i2i−2i2i0000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i000000000000
χ4222-2-2−2i2i−2i2i002200-2-22-22-2−2i2i−2i2i−2i2i−2i2i2002-2-2000000−2i2i−2i2i0000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i-222i−2i000000000000
χ4322-2-2−2i2i−2i2i002200-2-22-22-2−2i2i−2i2i−2i2i−2i2i2002-2-2000000−2i2i−2i2i000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i000000000000
χ4422-2-2−2i2i−2i2i002200-2-22-22-2−2i2i−2i2i−2i2i−2i2i2002-2-2000000−2i2i−2i2i000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i000000000000
χ452-2-2222-2-22-2222-222-2-2-2-2-2-2-2-2222222-2-2-22-222-22-2-2-2222-2002-200000000000000002i−2i2i−2i000000000000000000000000000000002i−2i2i−2i00000000
χ462-2-2222-2-22-2222-222-2-2-2-2-2-2-2-2222222-2-2-22-222-22-2-2-2222-2002-20000000000000000−2i2i−2i2i00000000000000000000000000000000−2i2i−2i2i00000000
χ472-2-2222-2-22-2-122-2-1211-2-211-2-2-1-122-1-1-211-112-112-211-1-1-1100-11−i3i300−i3i300−i3−i3i3i3−i3−i3i3i32i−2i2i−2i0000000000003−33−33−33−3000000000000−ii−ii00000000
χ482-2-2222-2-22-2-122-2-1211-2-211-2-2-1-122-1-1-211-112-112-211-1-1-1100-11−i3i300−i3i300−i3−i3i3i3−i3−i3i3i3−2i2i−2i2i000000000000−33−33−33−33000000000000i−ii−i00000000
χ492-2-2222-2-22-2-122-2-1211-2-211-2-2-1-122-1-1-211-112-112-211-1-1-1100-11i3−i300i3−i300i3i3−i3−i3i3i3−i3−i32i−2i2i−2i000000000000−33−33−33−33000000000000−ii−ii00000000
χ502-2-2222-2-22-2-122-2-1211-2-211-2-2-1-122-1-1-211-112-112-211-1-1-1100-11i3−i300i3−i300i3i3−i3−i3i3i3−i3−i3−2i2i−2i2i0000000000003−33−33−33−3000000000000i−ii−i00000000
χ512-2-2222-2-2-2222-2222-2-2-2-2-2-2-2-222222-22-2-222-2-22-22-2-222-2200-22000000000000000000002i−2i2i−2i000000000000000000000000000000002i−2i2i−2i0000
χ522-2-2222-2-2-2222-2222-2-2-2-2-2-2-2-222222-22-2-222-2-22-22-2-222-2200-2200000000000000000000−2i2i−2i2i00000000000000000000000000000000−2i2i−2i2i0000
χ532-2-2222-2-2-222-1-222-1-2-211-2-21122-1-1-1-2-111-121-221-111-1-11-1001-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i300002i−2i2i−2i00000000000000003−33−33−33−300000000−ii−ii0000
χ542-2-2222-2-2-222-1-222-1-2-211-2-21122-1-1-1-2-111-121-221-111-1-11-1001-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i30000−2i2i−2i2i0000000000000000−33−33−33−3300000000i−ii−i0000
χ552-2-2222-2-2-222-1-222-1-2-211-2-21122-1-1-1-2-111-121-221-111-1-11-1001-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i300002i−2i2i−2i0000000000000000−33−33−33−3300000000−ii−ii0000
χ562-2-2222-2-2-222-1-222-1-2-211-2-21122-1-1-1-2-111-121-221-111-1-11-1001-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i30000−2i2i−2i2i00000000000000003−33−33−33−300000000i−ii−i0000
χ572-2-22-2-2222-222-2222-2-2-2-22222-2-2-2-222-2-2-22-22-22-2222-2-22-200-22000000000000000000002i−2i−2i2i000000000000000000000000000000002i−2i−2i2i0000
χ582-2-22-2-2222-222-2222-2-2-2-22222-2-2-2-222-2-2-22-22-22-2222-2-22-200-2200000000000000000000−2i2i2i−2i00000000000000000000000000000000−2i2i2i−2i0000
χ592-2-22-2-2222-22-1-222-1-2-21122-1-1-2-211-12111-1-2-1-221-1-1-111-11001-1003−300−333−33−3−33−3300002i−2i−2i2i0000000000000000i3−i3i3−i3−i3i3−i3i300000000−iii−i0000
χ602-2-22-2-2222-22-1-222-1-2-21122-1-1-2-211-12111-1-2-1-221-1-1-111-11001-1003−300−333−33−3−33−330000−2i2i2i−2i0000000000000000−i3i3−i3i3i3−i3i3−i300000000i−i−ii0000
χ612-2-22-2-2222-22-1-222-1-2-21122-1-1-2-211-12111-1-2-1-221-1-1-111-11001-100−33003−3−33−333−33−300002i−2i−2i2i0000000000000000−i3i3−i3i3i3−i3i3−i300000000−iii−i0000
χ622-2-22-2-2222-22-1-222-1-2-21122-1-1-2-211-12111-1-2-1-221-1-1-111-11001-100−33003−3−33−333−33−30000−2i2i2i−2i0000000000000000i3−i3i3−i3−i3i3−i3i300000000i−i−ii0000
χ632-2-22-2-222-22222-222-2-2-2-22222-2-2-2-22-22-2-222-22-22-222-2-2-22002-200000000000000002i−2i−2i2i000000000000000000000000000000002i−2i−2i2i00000000
χ642-2-22-2-222-22222-222-2-2-2-22222-2-2-2-22-22-2-222-22-22-222-2-2-22002-20000000000000000−2i2i2i−2i00000000000000000000000000000000−2i2i2i−2i00000000
χ652-2-22-2-222-22-122-2-1211-2-2-1-12211-2-2-11211-1-1-2-112-2-1-1111-100-113−300−330033−3−3−3−3332i−2i−2i2i000000000000i3−i3i3−i3−i3i3−i3i3000000000000−iii−i00000000
χ662-2-22-2-222-22-122-2-1211-2-2-1-12211-2-2-11211-1-1-2-112-2-1-1111-100-113−300−330033−3−3−3−333−2i2i2i−2i000000000000−i3i3−i3i3i3−i3i3−i3000000000000i−i−ii00000000
χ672-2-22-2-222-22-122-2-1211-2-2-1-12211-2-2-11211-1-1-2-112-2-1-1111-100-11−33003−300−3−33333−3−32i−2i−2i2i000000000000−i3i3−i3i3i3−i3i3−i3000000000000−iii−i00000000
χ682-2-22-2-222-22-122-2-1211-2-2-1-12211-2-2-11211-1-1-2-112-2-1-1111-100-11−33003−300−3−33333−3−3−2i2i2i−2i000000000000i3−i3i3−i3−i3i3−i3i3000000000000i−i−ii00000000
χ694444444444-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2111-2-2-2-2-2-21111114411-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000000000
χ704444444444-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2111-2-2-2-2-2-2111111-4-41122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000
χ7144444444-4-44-2-4-44-244-2-244-2-244-2-2-2-42-2-2-2-42-4-422-2-2-2-22200220000000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.