Finite Group Databasebeta

← Group #13178262

Character table — Group #13178262

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order1222333446666666662333334666666666666666661212121212121212666666666666121212121212121212121212121212121212121212122244666622244444446666121212121212121212126121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1-1-1-1-111-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-11
χ5111111111111111111-111111-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-11-1-11-11-11-111-1-11111-1-11111-1-1-1-1
χ6111111111111111111-111111-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11-11-1-1-1-1-1-111-1-1-1-1-1-11111
χ7111111111111111111-111111-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-111111-1-1-1-11111-1-11-1-11
χ8111111111111111111-111111-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-111-1-1-11111-1-111-1-111-111-1
χ91111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-1-11-11111111-1-1-1-1-1-1-1-1-1-111
χ101111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-11-11-1-1-111-1-1-1-1-1-1111111-1-1
χ111111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11-111-111-1-1-1-11111-1-1111-11-1
χ121111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-11-1-1-1-111111111-1-1-11-11
χ131111111-1-1111111111-1111111-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1
χ141111111-1-1111111111-1111111-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-111
χ151111111-1-1111111111-1111111-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-11-1-1-1-1111111-1-111-1-1-1-111-11-11
χ161111111-1-1111111111-1111111-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-11-11-111-1-1-1-1111111-1-111-1-11-11-1
χ17222222-122-12222-1-12222-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1200002000000-1-100-1-1-1-100000000
χ18222222-122-12222-1-12222-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-20000-20000001100111100000000
χ19222222-122-12222-1-122-22-1-1-1-1-2112-1-1-1-122-1-1-1-1-1-1-1-122-1-11122-2-2-2-211111111-2-222-1-1-1-1-1-1-1-1-2-2111111112222-1-1-1-1-20000-20000001100-1-11100000000
χ20222222-122-12222-1-122-22-1-1-1-1-2112-1-1-1-122-1-1-1-1-1-1-1-122-1-11122-2-2-2-211111111-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2-2-21111200002000000-1-10011-1-100000000
χ21222222-1-2-2-12222-1-12222-1-1-1-1-2-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-2-22222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-21111111122-2-2-1-1-1-120000-2000000-1-100111100000000
χ22222222-1-2-2-12222-1-12222-1-1-1-1-2-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-2-22222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-211111111-2-2221111-2000020000001100-1-1-1-100000000
χ23222222-1-2-2-12222-1-122-22-1-1-1-12112-1-1-1-122-1-1-1-1-1-1-1-1-2-211-1-1-2-2-2-2-2-21111111122-2-21111111122-1-1-1-1-1-1-1-122-2-2-1-1-1-1-200002000000110011-1-100000000
χ24222222-1-2-2-12222-1-122-22-1-1-1-12112-1-1-1-122-1-1-1-1-1-1-1-1-2-211-1-1-2-2-2-2-2-21111111122-2-21111111122-1-1-1-1-1-1-1-1-2-222111120000-2000000-1-100-1-11100000000
χ2522222-122222-12-1222-12-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1222222-1-12-1-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000202002200-1-100000000-1-1000-1-10
χ2622222-122222-12-1222-12-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1222222-1-12-1-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000-20-200-2-200110000000011000110
χ2722222-122222-12-1222-1-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-12222-2-2-1-1-2111-2-21111111-2-1-122-1-1-1-1-1-111-2-211111100000000020-2002-200-1-100000000-1-1000110
χ2822222-122222-12-1222-1-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-12222-2-2-1-1-2111-2-21111111-2-1-122-1-1-1-1-1-111-2-2111111000000000-20200-2200110000000011000-1-10
χ2922222-12-2-222-12-1222-12-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2112-1-1-122-1-1-1-1-1-11-211-2-211111111-2-211111100000000020-200-2200-1-100000000110001-10
χ3022222-12-2-222-12-1222-12-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2112-1-1-122-1-1-1-1-1-11-211-2-211111111-2-2111111000000000-202002-2001100000000-1-1000-110
χ3122222-12-2-222-12-1222-1-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-22211-2111-2-2111111-1211-2-2111111-1-122-1-1-1-1-1-100000000020200-2-200-1-10000000011000-110
χ3222222-12-2-222-12-1222-1-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-22211-2111-2-2111111-1211-2-2111111-1-122-1-1-1-1-1-1000000000-20-20022001100000000-1-10001-10
χ332222-122222-12-1222-122-1-12-1-1222-1-12-1-1-1-1-1-122-1-1-1-1-1-1222222-12-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000202000220000-1-1000000-1-1-100-1
χ342222-122222-12-1222-122-1-12-1-1222-1-12-1-1-1-1-1-122-1-1-1-1-1-1222222-12-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000-20-2000-2-2000011000000111001
χ352222-122222-12-1222-12-2-1-12-1-1-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-2221-21111-2-21111-21-1-1-1-122-1-1-1-11111-2-21111000000000020-2000-2200001100000011-100-1
χ362222-122222-12-1222-12-2-1-12-1-1-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-2221-21111-2-21111-21-1-1-1-122-1-1-1-11111-2-211110000000000-2020002-20000-1-1000000-1-11001
χ372222-122-2-22-12-1222-122-1-12-1-1-222-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-211111-2-211111111-2-21111000000000020-20002-2000011000000-1-1-1001
χ382222-122-2-22-12-1222-122-1-12-1-1-222-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-211111-2-211111111-2-211110000000000-202000-220000-1-100000011100-1
χ392222-122-2-22-12-1222-12-2-1-12-1-12-2-2-1-12-1-1-1-1-1-122-1-1-1-111-2-222-2-21-21111-2-211112-11111-2-21111-1-1-1-122-1-1-1-10000000000202000-2-20000-1-100000011-1001
χ402222-122-2-22-12-1222-12-2-1-12-1-12-2-2-1-12-1-1-1-1-1-122-1-1-1-111-2-222-2-21-21111-2-211112-11111-2-21111-1-1-1-122-1-1-1-10000000000-20-200022000011000000-1-1100-1
χ4122-2-22222i−2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i002i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-22i−2i22-2-200000000000000002i−2i0000000000
χ4222-2-22222i−2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i002i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-22−2i2i-2-2220000000000000000−2i2i0000000000
χ4322-2-2222−2i2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i00−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-2−2i2i22-2-20000000000000000−2i2i0000000000
χ4422-2-2222−2i2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i00−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-222i−2i-2-22200000000000000002i−2i0000000000
χ4522-2-222-12i−2i-1-2-22211-2-202-1-1-1-10−i3i32-1-1-1-1-2-2111111112i−2i−ii3−32i−2i0000−i3i3−i3i3−i3−i3i3i3002i−2i−ii−ii−i−iii003−33−333−3−32-22i−2i-1-111000000000000−i3i300−ii3−300000000
χ4622-2-222-12i−2i-1-2-22211-2-202-1-1-1-10−i3i32-1-1-1-1-2-2111111112i−2i−ii3−32i−2i0000−i3i3−i3i3−i3−i3i3i3002i−2i−ii−ii−i−iii003−33−333−3−3-22−2i2i11-1-1000000000000i3−i300i−i−3300000000
χ4722-2-222-12i−2i-1-2-22211-2-202-1-1-1-10i3−i32-1-1-1-1-2-2111111112i−2i−ii−332i−2i0000i3−i3i3−i3i3i3−i3−i3002i−2i−ii−ii−i−iii00−33−33−3−3332-22i−2i-1-111000000000000i3−i300−ii−3300000000
χ4822-2-222-12i−2i-1-2-22211-2-202-1-1-1-10i3−i32-1-1-1-1-2-2111111112i−2i−ii−332i−2i0000i3−i3i3−i3i3i3−i3−i3002i−2i−ii−ii−i−iii00−33−33−3−333-22−2i2i11-1-1000000000000−i3i300i−i3−300000000
χ4922-2-222-1−2i2i-1-2-22211-2-202-1-1-1-10−i3i32-1-1-1-1-2-211111111−2i2ii−i−33−2i2i0000−i3i3−i3i3−i3−i3i3i300−2i2ii−ii−iii−i−i00−33−33−3−3332-2−2i2i-1-111000000000000−i3i300i−i−3300000000
χ5022-2-222-1−2i2i-1-2-22211-2-202-1-1-1-10−i3i32-1-1-1-1-2-211111111−2i2ii−i−33−2i2i0000−i3i3−i3i3−i3−i3i3i300−2i2ii−ii−iii−i−i00−33−33−3−333-222i−2i11-1-1000000000000i3−i300−ii3−300000000
χ5122-2-222-1−2i2i-1-2-22211-2-202-1-1-1-10i3−i32-1-1-1-1-2-211111111−2i2ii−i3−3−2i2i0000i3−i3i3−i3i3i3−i3−i300−2i2ii−ii−iii−i−i003−33−333−3−32-2−2i2i-1-111000000000000i3−i300i−i3−300000000
χ5222-2-222-1−2i2i-1-2-22211-2-202-1-1-1-10i3−i32-1-1-1-1-2-211111111−2i2ii−i3−3−2i2i0000i3−i3i3−i3i3i3−i3−i300−2i2ii−ii−iii−i−i003−33−333−3−3-222i−2i11-1-1000000000000−i3i300−ii−3300000000
χ5344444-2-244-24-24-2-2-24-24-2-21114-2-2-2-2111-2-2-2-211111144-2-2-2-2-2-24-2-2-2-2-2111111-24-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5444444-2-244-24-24-2-2-24-2-4-2-2111-422-2-2111-2-2-2-211111144-2-222-2-2-422222-1-1-1-1-1-12-4-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-2-2-4-4-24-24-2-2-24-24-2-2111-4-2-2-2-2111-2-2-2-2111111-4-42222224-2-2-2-2-21111112-42222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5644444-2-2-4-4-24-24-2-2-24-2-4-2-2111422-2-2111-2-2-2-2111111-4-422-2-222-422222-1-1-1-1-1-1-242222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ574444-24-244-2-24-24-2-2-244-21-2114-2-2-21-211-2-211-2-21111-2-2-2-2-2-244-24-2-211-2-211114-2-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ584444-24-244-2-24-24-2-2-24-4-21-211-422-21-211-2-211-2-21111-2-2-2-222442-422-1-122-1-1-1-1-42-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ594444-24-2-4-4-2-24-24-2-2-244-21-211-4-2-2-21-211-2-211-2-21111222222-4-4-24-2-211-2-21111-4222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ604444-24-2-4-4-2-24-24-2-2-24-4-21-211422-21-211-2-211-2-211112222-2-2-4-42-422-1-122-1-1-1-14-222-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ614444-2-24444-2-2-2-244-2-241-2-2114441-2-21111-2-2-2-21111-2-24444-2-2-2-211-2-2-2-21111-2-211-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ624444-2-24444-2-2-2-244-2-2-41-2-211-4-4-41-2-21111-2-2-2-21111-2-244-4-4-2-222-1-12222-1-1-1-12211-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ634444-2-24-4-44-2-2-2-244-2-241-2-211-4441-2-21111-2-2-2-2111122-4-4-4-422-2-211-2-2-2-2111122-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ644444-2-24-4-44-2-2-2-244-2-2-41-2-2114-4-41-2-21111-2-2-2-2111122-4-4442222-1-12222-1-1-1-1-2-2-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
χ654444-2-2-244-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i324-2-2111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000
χ664444-2-2-244-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i324-2-2111−1+3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000000
χ674444-2-2-244-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i32-422111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-222-2-222-1-1-1-1-1-11+3i321−3i321+3i321−3i3222111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000000
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χ1208-8-88-4-4-40044-4444-4-440222−1+3i3−1−3i3000-2-2-21−3i31+3i3-22-22-221−3i3−1+3i31+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.