Finite Group Databasebeta

← Group #13178462

Character table — Group #13178462

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size112222222222244444444444444444444444444444444448888888888888888888888888888888888181818181818181818183636363636363636363636363636367272727272727272
order1223334466612123333366666666881212121212121212121212121212122424242466666121212121224242424242424242424242424242424242424242424242422448824242424224444446681212242466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1-1-1-1-11-1-1-1111
χ511111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-111-111-111-1-11-11-1-111-1
χ611111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-111-1-1111-111-1-1-11-111-1-11
χ711111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-11-1-111111-1-1-1-11
χ811111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-11-1-111-1-1-11111-1
χ911-1111-111111111111-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111111111-11-11-1-11-1-11-1-1-111-11-11-1-1
χ1011-1111-111111111111-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111-1-11-11-1111-1-11-1-1-1-1-11-11-111
χ1111-1111-111111111111-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11-1-11-1-111-111-11111-1-11-1-111
χ1211-1111-111111111111-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111-111-1-1-111-1111-111-111-1-1
χ1311-1111-111111111111-1-1-111111-11-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1-1-1-1-11-1-1-111-111-111-1111-1-1-111-11
χ1411-1111-111111111111-1-1-111111-11-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1-1-1-1-1-1111-1-11-11-111-111-1111-1-11-1
χ1511-1111-111111111111-1-1-111111-11-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-1111111111-1-11-11-1-11-1-11-1-111-1-11-11-1
χ1611-1111-111111111111-1-1-111111-11-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11111111-1-111-11-11-11-1-11-1-1-1-111-11-11
χ17222222-2-2222-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022222-2-2-2-2-20000000000000000000000002-2-22000000000000002-20-220000000000
χ18222222-2-2222-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022222-2-2-2-2-2000000000000000000000000-222-200000000000000-2202-20000000000
χ1922222-12222-1222-1-1-1-122-12-1-1-1-12222-12-122-1-1-1-1-1-1-1-122222-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-100000000000200022200000000-1000-1-1-1
χ2022222-12222-1222-1-1-1-122-12-1-1-1-12222-12-122-1-1-1-1-1-1-1-122222-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-100000000000-2000-2-2-2000000001000111
χ2122222-12222-1222-1-1-1-122-12-1-1-1-1-2-222-12-122-1-1-1-1-1-1-1-1-2-2-2-22-1-1-1-12-1-1-1-1-2-2-2111111111-2-2-2111111111000000000002000-2-2200000000-100011-1
χ2222222-12222-1222-1-1-1-122-12-1-1-1-1-2-222-12-122-1-1-1-1-1-1-1-1-2-2-2-22-1-1-1-12-1-1-1-1-2-2-2111111111-2-2-211111111100000000000-200022-2000000001000-1-11
χ232222-12222-1222-12-1-1-12-12-12-1-1-1222-12-12-1-122-1-1-1-1-1-12222-12-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000000202220000000000-10-1-1-1000
χ242222-12222-1222-12-1-1-12-12-12-1-1-1222-12-12-1-122-1-1-1-1-1-12222-12-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000000-20-2-2-2000000000010111000
χ252222-12222-1222-12-1-1-12-12-12-1-1-1-2-22-12-12-1-122-1-1-1-1-1-1-2-2-2-2-12-1-1-1-12-1-1-1111-2-2-2111111111-2-2-21111110000000000202-2-20000000000-10-111000
χ262222-12222-1222-12-1-1-12-12-12-1-1-1-2-22-12-12-1-122-1-1-1-1-1-1-2-2-2-2-12-1-1-1-12-1-1-1111-2-2-2111111111-2-2-21111110000000000-20-2220000000000101-1-1000
χ27222-12222-122-1-1-1-12-1-1-122-1-12-1-122-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-12-1-1-1-12-1-12-1-12-1-122-1-1-1-12-1-12-1-122-1-1-1-1222222-1-1-1-100000000-1-12-1-1-1-100000000
χ28222-12222-122-1-1-1-12-1-1-122-1-12-1-122-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-12-1-1-1-12-1-12-1-12-1-122-1-1-1-12-1-12-1-122-1-1-1-1-2-2-2-2-2-211110000000011-2111100000000
χ29222-12222-122-1-1-1-12-1-1-122-1-12-1-1-2-2-12222-1-1-1-122-1-1-1-11111-1-12-1-1-1-12-1-1-211-211-2-21111-211-211-2-211112222-2-2111100000000-1-1-2-1-11100000000
χ30222-12222-122-1-1-1-12-1-1-122-1-12-1-1-2-2-12222-1-1-1-122-1-1-1-11111-1-12-1-1-1-12-1-1-211-211-2-21111-211-211-2-21111-2-2-2-222-1-1-1-10000000011211-1-100000000
χ31222-122-2-2-12211-1-12-1-1-122-1-12-1-1001-2-2-2-21111-2-211113−33−3-1-12-1-111-21103−303−30033−3−303−303−30033−3−32-2-220033−3−300000000-1101-13−300000000
χ32222-122-2-2-12211-1-12-1-1-122-1-12-1-1001-2-2-2-21111-2-211113−33−3-1-12-1-111-21103−303−30033−3−303−303−30033−3−3-222-200−3−333000000001-10-11−3300000000
χ33222-122-2-2-12211-1-12-1-1-122-1-12-1-1001-2-2-2-21111-2-21111−33−33-1-12-1-111-2110−330−3300−3−3330−330−3300−3−3332-2-2200−3−33300000000-1101-1−3300000000
χ34222-122-2-2-12211-1-12-1-1-122-1-12-1-1001-2-2-2-21111-2-21111−33−33-1-12-1-111-2110−330−3300−3−3330−330−3300−3−333-222-20033−3−3000000001-10-113−300000000
χ3522-22222-2222-2-222222-2-2-22222200222-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-2-22222200000000000000000000000022-2-200000000000000220-2-20000000000
χ3622-22222-2222-2-222222-2-2-22222200222-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-2-222222000000000000000000000000-2-22200000000000000-2-20220000000000
χ3722-222-1-2222-1222-1-1-1-1-2-212-1-1-1-12-2-2-212-122-1-1-1-1-1-1-1-122-2-2-21111-21111222-1-1-1-1-1-1-1-1-1-2-2-21111111110000000000020002-2-200000000-1000-111
χ3822-222-1-2222-1222-1-1-1-1-2-212-1-1-1-12-2-2-212-122-1-1-1-1-1-1-1-122-2-2-21111-21111222-1-1-1-1-1-1-1-1-1-2-2-211111111100000000000-2000-2220000000010001-1-1
χ3922-222-1-2222-1222-1-1-1-1-2-212-1-1-1-1-22-2-212-122-1-1-1-1-1-1-1-1-2-222-21111-21111-2-2-2111111111222-1-1-1-1-1-1-1-1-1000000000002000-22-200000000-10001-11
χ4022-222-1-2222-1222-1-1-1-1-2-212-1-1-1-1-22-2-212-122-1-1-1-1-1-1-1-1-2-222-21111-21111-2-2-2111111111222-1-1-1-1-1-1-1-1-100000000000-20002-22000000001000-11-1
χ4122-22-12-222-1222-12-1-1-1-21-2-12-1-1-12-2-21-2-12-1-122-1-1-1-1-1-122-2-21-21111-2111-1-1-1222-1-1-1-1-1-1111-2-2-2111111000000000020-22-20000000000-101-11000
χ4222-22-12-222-1222-12-1-1-1-21-2-12-1-1-12-2-21-2-12-1-122-1-1-1-1-1-122-2-21-21111-2111-1-1-1222-1-1-1-1-1-1111-2-2-21111110000000000-202-22000000000010-11-1000
χ4322-22-12-222-1222-12-1-1-1-21-2-12-1-1-1-22-21-2-12-1-122-1-1-1-1-1-1-2-2221-21111-2111111-2-2-2111111-1-1-1222-1-1-1-1-1-1000000000020-2-220000000000-1011-1000
χ4422-22-12-222-1222-12-1-1-1-21-2-12-1-1-1-22-21-2-12-1-122-1-1-1-1-1-1-2-2221-21111-2111111-2-2-2111111-1-1-1222-1-1-1-1-1-10000000000-2022-2000000000010-1-11000
χ4522-2-1222-2-12211-1-12-1-11-2-2-1-12-1-100-122-2-21111-2-211113−3−3311-211-1-12-1-103−303−30033−3−30−330−3300−3−33322-2-20033−3−300000000-1-1011−3300000000
χ4622-2-1222-2-12211-1-12-1-11-2-2-1-12-1-100-122-2-21111-2-211113−3−3311-211-1-12-1-103−303−30033−3−30−330−3300−3−333-2-22200−3−33300000000110-1-13−300000000
χ4722-2-1222-2-12211-1-12-1-11-2-2-1-12-1-100-122-2-21111-2-21111−333−311-211-1-12-1-10−330−3300−3−33303−303−30033−3−322-2-200−3−33300000000-1-10113−300000000
χ4822-2-1222-2-12211-1-12-1-11-2-2-1-12-1-100-122-2-21111-2-21111−333−311-211-1-12-1-10−330−3300−3−33303−303−30033−3−3-2-2220033−3−300000000110-1-1−3300000000
χ4922-2-122-22-122-1-1-1-12-1-11-2-2-1-12-1-12-21-2-222-1-1-1-122-1-1-1-1-1-11111-21111-2112-1-12-1-122-1-1-1-1-211-211-2-211112-22-222-1-1-1-100000000-11-2-111100000000
χ5022-2-122-22-122-1-1-1-12-1-11-2-2-1-12-1-12-21-2-222-1-1-1-122-1-1-1-1-1-11111-21111-2112-1-12-1-122-1-1-1-1-211-211-2-21111-22-22-2-21111000000001-121-1-1-100000000
χ5122-2-122-22-122-1-1-1-12-1-11-2-2-1-12-1-1-221-2-222-1-1-1-122-1-1-1-111-1-111-21111-211-211-211-2-211112-1-12-1-122-1-1-1-12-22-2-2-2111100000000-112-11-1-100000000
χ5222-2-122-22-122-1-1-1-12-1-11-2-2-1-12-1-1-221-2-222-1-1-1-122-1-1-1-111-1-111-21111-211-211-211-2-211112-1-12-1-122-1-1-1-1-22-2222-1-1-1-1000000001-1-21-11100000000
χ5344444-2-4-444-2-4-44-2-2-2-244-24-2-2-2-200-4-42-42-4-42222222200004-2-2-2-2-42222000000000000000000000000000000000000000000000000000000000
χ544444-24-4-44-24-4-4-24-2-2-24-24-24-2-2-200-42-42-422-4-42222220000-24-2-2-22-4222000000000000000000000000000000000000000000000000000000000
χ554444-2-2444-2-244-2-21114-2-2-2-2111444-2-2-2-2-2-2-2-21111114444-2-2111-2-2111-2-2-2-2-2-2111111-2-2-2-2-2-2111111000000000000000000000000000000000
χ564444-2-2444-2-244-2-21114-2-2-2-2111-4-44-2-2-2-2-2-2-2-2111111-4-4-4-4-2-2111-2-2111222222-1-1-1-1-1-1222222-1-1-1-1-1-1000000000000000000000000000000000
χ574444-2-2-4-44-2-2-4-4-2-21114-2-2-2-211100-422222222-1-1-1-1-1-10000-2-211122-1-1-10000003i−3i3i−3i3i−3i0000003i−3i3i−3i3i−3i000000000000000000000000000000000
χ584444-2-2-4-44-2-2-4-4-2-21114-2-2-2-211100-422222222-1-1-1-1-1-10000-2-211122-1-1-1000000−3i3i−3i3i−3i3i000000−3i3i−3i3i−3i3i000000000000000000000000000000000
χ59444-24-244-24-2-2-2-21-211-24-2-21-21144-24-24-2-2-211-2-21111-2-2-2-2-21-211-21-2114-2-2-211-2-211114-2-2-211-2-21111000000000000000000000000000000000
χ60444-24-244-24-2-2-2-21-211-24-2-21-211-4-4-24-24-2-2-211-2-211112222-21-211-21-211-4222-1-122-1-1-1-1-4222-1-122-1-1-1-1000000000000000000000000000000000
χ61444-24-2-4-4-24-222-21-211-24-2-21-211002-42-4222-1-122-1-1-1-123−2323−23-21-2112-12-1-1023−230−3300−3−333023−230−3300−3−333000000000000000000000000000000000
χ62444-24-2-4-4-24-222-21-211-24-2-21-211002-42-4222-1-122-1-1-1-1−2323−2323-21-2112-12-1-10−232303−30033−3−30−232303−30033−3−3000000000000000000000000000000000
χ63444-2-2444-2-24-2-21-2-211-2-241-2-21144-2-24-2411-2-2-2-21111-2-2-2-21-2-2111-2-211-2114-2-2-2-21111-2114-2-2-2-21111000000000000000000000000000000000
χ64444-2-2444-2-24-2-21-2-211-2-241-2-211-4-4-2-24-2411-2-2-2-2111122221-2-2111-2-2112-1-1-42222-1-1-1-12-1-1-42222-1-1-1-1000000000000000000000000000000000
χ65444-2-24-4-4-2-24221-2-211-2-241-2-2110022-42-4-1-12222-1-1-1-123−2323−231-2-211-122-1-10−33023−2300−3−3330−33023−2300−3−333000000000000000000000000000000000
χ66444-2-24-4-4-2-24221-2-211-2-241-2-2110022-42-4-1-12222-1-1-1-1−2323−23231-2-211-122-1-103−30−23230033−3−303−30−23230033−3−3000000000000000000000000000000000
χ67444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i3244-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-211-21111−1−3i32−1+3i32−1+3i32−1−3i32-211-21111−1−3i32−1+3i32−1+3i32−1−3i32000000000000000000000000000000000
χ68444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i32-4-4-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i322222111−1−3i32−1+3i32111−1−3i32−1+3i322-1-12-1-1-1-11+3i321−3i321−3i321+3i322-1-12-1-1-1-11+3i321−3i321−3i321+3i32000000000000000000000000000000000
χ69444-2-2-244-2-2-2-2-2111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i3244-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-211-21111−1+3i32−1−3i32−1−3i32−1+3i32-211-21111−1+3i32−1−3i32−1−3i32−1+3i32000000000000000000000000000000000
χ70444-2-2-244-2-2-2-2-2111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i32-4-4-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i322222111−1+3i32−1−3i32111−1+3i32−1−3i322-1-12-1-1-1-11−3i321+3i321+3i321−3i322-1-12-1-1-1-11−3i321+3i321+3i321−3i32000000000000000000000000000000000
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χ72444-2-2-2-4-4-2-2-222111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i320022222-1-1-1-1-1-11+3i321+3i321−3i321−3i32−2323−2323111−1−3i32−1+3i32-1-1-11+3i321−3i3203−303−3−3i3i−ζ14−2ζ222ζ14+ζ22−2ζ14−ζ22ζ14+2ζ2203−303−3−3i3i−ζ14−2ζ222ζ14+ζ22−2ζ14−ζ22ζ14+2ζ22000000000000000000000000000000000
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χ1118-80-4-4-40044443−43222−1−3i3−1+3i3000-2-2-21+3i31−3i30000000−2323−23236i−6i2ζ14+4ζ22−2ζ14−4ζ22−4ζ14−2ζ224ζ14+2ζ2200000000000000000000000000000000000000000000000000000000000000000000000
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χ1138-80-4-4-400444−4343222−1−3i3−1+3i3000-2-2-21+3i31−3i3000000023−2323−23−6i6i−2ζ14−4ζ222ζ14+4ζ224ζ14+2ζ22−4ζ14−2ζ2200000000000000000000000000000000000000000000000000000000000000000000000
χ1148-80-4-4-400444−4343222−1+3i3−1−3i3000-2-2-21−3i31+3i3000000023−2323−236i−6i4ζ14+2ζ22−4ζ14−2ζ22−2ζ14−4ζ222ζ14+4ζ2200000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.