Finite Group Databasebeta

← Group #13178776

Character table — Group #13178776

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size112222222222244444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636363636363636363636363636727272727272
order1223334466612122333334666666666612121212121212121212121212121212126666666666666666612121212121212121212121212121212122244882224446688812121212121224242424666122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111-1-11-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111
χ51111111111111-111111-111-1-1111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-111
χ61111111111111-111111-111-1-1111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ71111111111111-111111-111-1-1111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-11-1-1-1-111111111-111-1-1-1
χ81111111111111-111111-111-1-1111111111-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-111-1-11111-1-1-1-11-1-1111
χ911-1111-11111-1-1111111-1-1-111-111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-11-11-111-11-11-111-1-11-11-111-1-111-1-1-11-111-1
χ1011-1111-11111-1-1111111-1-1-111-111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11-111-1-11-11-111-111-1-1-1-1111-11-1-11
χ1111-1111-11111-1-1111111-1-1-111-111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-11-111-11-1-11-11-1-11111-1-1-1-111-11
χ1211-1111-11111-1-1111111-1-1-111-111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11-1-1111-1-11-1-111-1-11111-1-11-1
χ1311-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-11-1111-11-11-11-1-11-11-1-1-11111-1-11-11-11-1
χ1411-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-11-1-1-1-11-1-1111-11-111-1-1-111-1-111-11-11-11
χ1511-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-111111-11-1-1-11-1-11-1111-1-111-1-111-1-1-11
χ1611-1111-11111-1-1-1111111-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-11-1-1-1-111-11-1111-1-1111-1-1-1-111-1-1111-1
χ17222222-2-2222-2-202222202200222222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-200000000002-2-22000000002-2000-2200000000000000
χ18222222-2-2222-2-202222202200222222-2-2-200-2-2-2-2-2-2-2-2-2-2-2-20022222000000000000-2-2-2-2-20000000000-222-200000000-220002-200000000000000
χ1922222-122-1222222-1-1-1-122222-12-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000000220000002200000000000-1-10-1-1
χ2022222-122-1222222-1-1-1-122222-12-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000000-2-2000000-2-20000000000011011
χ2122222-122-12222-22-1-1-1-1-222-2-2-12-1-1-1-1-122-2-222-1-1-1-1-1-1-1-1-12-212-1-1-1-1-2-2111111111-22-1-1-1-1-2-211111111000000022000000-2-200000000000-1-1011
χ2222222-122-12222-22-1-1-1-1-222-2-2-12-1-1-1-1-122-2-222-1-1-1-1-1-1-1-1-12-212-1-1-1-1-2-2111111111-22-1-1-1-1-2-2111111110000000-2-20000002200000000000110-1-1
χ232222-122222-1222-12-1-1-122-1-1-12-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-122-1-1-1-1-1-1222200000220-1-1000-1-1-1-1-1-10000000000
χ242222-122222-1222-12-1-1-122-1-1-12-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200000-2-20110001111110000000000
χ252222-122222-122-2-12-1-1-1-22-1112-12-1-1-12-1-111-1-122-1-1-1-1-1-122-2-2-12-1-1-111-2-2111111-2-2-12-1-1-111-2-2111111222200000-2-20-1-1000-1-111110000000000
χ262222-122222-122-2-12-1-1-1-22-1112-12-1-1-12-1-111-1-122-1-1-1-1-1-122-2-2-12-1-1-111-2-2111111-2-2-12-1-1-111-2-2111111-2-2-2-2000002201100011-1-1-1-10000000000
χ272222-12-2-222-1-2-20-12-1-1-102-1−i3i32-12-1-1-1-211−i3i311-2-2111111-2-200-12-1-1-1−i3i300−i3−i3−i3i3i3i3001-2111−i3i300−i3−i3−i3i3i3i32-2-2200000000-110001-1−i3i3−i3i30000000000
χ282222-12-2-222-1-2-20-12-1-1-102-1−i3i32-12-1-1-1-211−i3i311-2-2111111-2-200-12-1-1-1−i3i300−i3−i3−i3i3i3i3001-2111−i3i300−i3−i3−i3i3i3i3-222-2000000001-1000-11i3−i3i3−i30000000000
χ292222-12-2-222-1-2-20-12-1-1-102-1i3−i32-12-1-1-1-211i3−i311-2-2111111-2-200-12-1-1-1i3−i300i3i3i3−i3−i3−i3001-2111i3−i300i3i3i3−i3−i3−i32-2-2200000000-110001-1i3−i3i3−i30000000000
χ302222-12-2-222-1-2-20-12-1-1-102-1i3−i32-12-1-1-1-211i3−i311-2-2111111-2-200-12-1-1-1i3−i300i3i3i3−i3−i3−i3001-2111i3−i300i3i3i3−i3−i3−i3-222-2000000001-1000-11−i3i3−i3i30000000000
χ31222-122222-12-1-12-1-12-1-12-12222-1-12-1-122222-1-1-1-122-1-1-1-12-1-12-1-12-1-1-1-1-1-12-1-12-1-12-1-1-12-1-1-1-1-1-12-1-12-1-100002220000200200000000-1-1-1-1-100-100
χ32222-122222-12-1-12-1-12-1-12-12222-1-12-1-122222-1-1-1-122-1-1-1-12-1-12-1-12-1-1-1-1-1-12-1-12-1-12-1-1-12-1-1-1-1-1-12-1-12-1-10000-2-2-20000-200-2000000001111100100
χ33222-122222-12-1-1-2-1-12-1-1-2-12-2-22-1-12-1-1222-2-2-1-1-1-122-1-1-1-12-11-2-1-12-1-11111-211-211-21-1-12-1-11111-211-211000022-20000-200200000000-1-1-1-1100100
χ34222-122222-12-1-1-2-1-12-1-1-2-12-2-22-1-12-1-1222-2-2-1-1-1-122-1-1-1-12-11-2-1-12-1-11111-211-211-21-1-12-1-11111-211-2110000-2-220000200-2000000001111-100-100
χ3522-22222-2222220222220-2-200-2222222-22002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-2000000000022-2-20000000022000-2-200000000000000
χ3622-22222-2222220222220-2-200-2222222-22002222222222-2-200-2-2-2-2-2000000000000-2-2-2-2-20000000000-2-22200000000-2-20002200000000000000
χ3722-222-1-22-122-2-222-1-1-1-1-2-2-22212-1-1-1-112-2-2-2-2-211111111-122-1-2111122-1-1-1-1-1-1-1-11-22-1-1-1-1-2-21111111100000002-20000002-200000000000-110-11
χ3822-222-1-22-122-2-222-1-1-1-1-2-2-22212-1-1-1-112-2-2-2-2-211111111-122-1-2111122-1-1-1-1-1-1-1-11-22-1-1-1-1-2-2111111110000000-22000000-22000000000001-101-1
χ3922-222-1-22-122-2-2-22-1-1-1-12-2-2-2-212-1-1-1-112-222-2-211111111-12-21-21111-2-211111111-122-1-1-1-122-1-1-1-1-1-1-1-100000002-2000000-2200000000000-1101-1
χ4022-222-1-22-122-2-2-22-1-1-1-12-2-2-2-212-1-1-1-112-222-2-211111111-12-21-21111-2-211111111-122-1-1-1-122-1-1-1-1-1-1-1-10000000-220000002-2000000000001-10-11
χ4122-22-122-222-1220-12-1-1-10-21−i3i3-2-12-1-1-121-1i3−i3-1-122-1-1-1-1-1-1-2-2001-2111−i3i300−i3−i3−i3i3i3i3001-2111i3−i300i3i3i3−i3−i3−i322-2-200000000-1-100011−i3i3i3−i30000000000
χ4222-22-122-222-1220-12-1-1-10-21−i3i3-2-12-1-1-121-1i3−i3-1-122-1-1-1-1-1-1-2-2001-2111−i3i300−i3−i3−i3i3i3i3001-2111i3−i300i3i3i3−i3−i3−i3-2-2220000000011000-1-1i3−i3−i3i30000000000
χ4322-22-122-222-1220-12-1-1-10-21i3−i3-2-12-1-1-121-1−i3i3-1-122-1-1-1-1-1-1-2-2001-2111i3−i300i3i3i3−i3−i3−i3001-2111−i3i300−i3−i3−i3i3i3i322-2-200000000-1-100011i3−i3−i3i30000000000
χ4422-22-122-222-1220-12-1-1-10-21i3−i3-2-12-1-1-121-1−i3i3-1-122-1-1-1-1-1-1-2-2001-2111i3−i300i3i3i3−i3−i3−i3001-2111−i3i300−i3−i3−i3i3i3i3-2-2220000000011000-1-1−i3i3i3−i30000000000
χ4522-22-12-2222-1-2-22-12-1-1-1-2-21-1-1-2-12-1-1-1-2-111111-2-211111122221-2111-1-122-1-1-1-1-1-1-2-2-12-1-1-111-2-21111112-22-2000002-20-11000-11-1-1110000000000
χ4622-22-12-2222-1-2-22-12-1-1-1-2-21-1-1-2-12-1-1-1-2-111111-2-211111122221-2111-1-122-1-1-1-1-1-1-2-2-12-1-1-111-2-2111111-22-2200000-2201-10001-111-1-10000000000
χ4722-22-12-2222-1-2-2-2-12-1-1-12-2111-2-12-1-1-1-2-11-1-111-2-211111122-2-21-211111-2-211111122-12-1-1-1-1-122-1-1-1-1-1-12-22-200000-220-11000-1111-1-10000000000
χ4822-22-12-2222-1-2-2-2-12-1-1-12-2111-2-12-1-1-1-2-11-1-111-2-211111122-2-21-211111-2-211111122-12-1-1-1-1-122-1-1-1-1-1-1-22-22000002-201-10001-1-1-1110000000000
χ4922-2-122-222-12112-1-12-1-1-21-222-2-1-12-1-1-22-2-2-21111-2-211112-1-1211-211-1-1-1-12-1-12-1-1-21-1-12-1-11111-211-211000022-20000200-200000000-1-111100-100
χ5022-2-122-222-12112-1-12-1-1-21-222-2-1-12-1-1-22-2-2-21111-2-211112-1-1211-211-1-1-1-12-1-12-1-1-21-1-12-1-11111-211-2110000-2-220000-20020000000011-1-1-100100
χ5122-2-122-222-1211-2-1-12-1-121-2-2-2-2-1-12-1-1-22-2221111-2-211112-11-211-2111111-211-2112-1-1-12-1-1-1-1-1-12-1-12-1-100002220000-200-200000000-1-111-100100
χ5222-2-122-222-1211-2-1-12-1-121-2-2-2-2-1-12-1-1-22-2221111-2-211112-11-211-2111111-211-2112-1-1-12-1-1-1-1-1-12-1-12-1-10000-2-2-2000020020000000011-1-1100-100
χ5344444-2-4-4-244-4-404-2-2-2-204400-24-2-2-2-22-4-400-4-4222222222-4004-2-2-2-2000000000000-422220000000000000000000000000000000000000000000
χ544444-2-244-24-2444-2-211144-2-2-2-2-2-2111-2-2-2-2-2-2-2-2-2111111-244-2-2-2111-2-2-2-2111111-24-2-2111-2-2-2-2111111000000000000000000000000000000000
χ554444-2-244-24-244-4-2-2111-44-222-2-2-2111-2-2-222-2-2-2-2111111-24-42-2-21112222-1-1-1-1-1-12-4-2-21112222-1-1-1-1-1-1000000000000000000000000000000000
χ564444-2-2-4-4-24-2-4-40-2-211104-2−2i32i3-2-2-2111222−2i32i32222-1-1-1-1-1-12-400-2-2111−2i32i300i3i3i3−i3−i3−i30022-1-1-1−2i32i300i3i3i3−i3−i3−i3000000000000000000000000000000000
χ574444-2-2-4-4-24-2-4-40-2-211104-22i3−2i3-2-2-21112222i3−2i32222-1-1-1-1-1-12-400-2-21112i3−2i300−i3−i3−i3i3i3i30022-1-1-12i3−2i300−i3−i3−i3i3i3i3000000000000000000000000000000000
χ58444-244-4-44-24220-2-24-2-20-24004-2-24-2-2-4-4-4002222-4-42222-4200-2-24-2-200000000000022-4220000000000000000000000000000000000000000000
χ59444-24-244-2-24-2-24-21-2114-2444-2-21-211-24444-2-211-2-21111-2-2-2-2-21-211-2-211-211-211-2-2-21-211-2-211-211-211000000000000000000000000000000000
χ60444-24-244-2-24-2-2-4-21-211-4-24-4-4-2-21-211-244-4-4-2-211-2-21111-2-222-21-21122-1-12-1-12-1-122-21-21122-1-12-1-12-1-1000000000000000000000000000000000
χ61444-24-2-4-4-2-24220-21-2110-2400-2-21-2112-4-40022-1-122-1-1-1-12200-21-211003-303-303-3002-12-1-1003-303-303-3000000000000000000000000000000000
χ62444-24-2-4-4-2-24220-21-2110-2400-2-21-2112-4-40022-1-122-1-1-1-12200-21-21100-330-330-33002-12-1-100-330-330-33000000000000000000000000000000000
χ63444-2-24444-2-2-2-241-2-2114-2-2-2-241-2-2114-2-2-2-211-2-2-2-211114-2-241-2-21111-2-2-211-2114-21-2-21111-2-2-211-211000000000000000000000000000000000
χ64444-2-24444-2-2-2-2-41-2-211-4-2-22241-2-2114-2-22211-2-2-2-211114-22-41-2-211-1-1222-1-12-1-1-421-2-211-1-1222-1-12-1-1000000000000000000000000000000000
χ65444-2-24-4-44-2-22201-2-2110-2-2−2i32i341-2-211-422−2i32i3-1-12222-1-1-1-1-42001-2-211i3−i300−2i3i3i32i3−i3−i300-122-1-1i3−i300−2i3i3i32i3−i3−i3000000000000000000000000000000000
χ66444-2-24-4-44-2-22201-2-2110-2-22i3−2i341-2-211-4222i3−2i3-1-12222-1-1-1-1-42001-2-211−i3i3002i3−i3−i3−2i3i3i300-122-1-1−i3i3002i3−i3−i3−2i3i3i3000000000000000000000000000000000
χ67444-2-2-244-2-2-2-2-24111−1−3i32−1+3i324-2-2-2-2-2111−1−3i32−1+3i32-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2111−1−3i32−1+3i3211111−1−3i32−1+3i321−1+3i32−1−3i32-2-2111−1−3i32−1+3i3211111−1−3i32−1+3i321−1+3i32−1−3i32000000000000000000000000000000000
χ68444-2-2-244-2-2-2-2-24111−1+3i32−1−3i324-2-2-2-2-2111−1+3i32−1−3i32-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2111−1+3i32−1−3i3211111−1+3i32−1−3i321−1−3i32−1+3i32-2-2111−1+3i32−1−3i3211111−1+3i32−1−3i321−1−3i32−1+3i32000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.