Finite Group Databasebeta

← Group #13173337

Character table — Group #13173337

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order122222366633333344666666666666666666661212121266666666666612121212121212121212121212121212121212121212121244444412121212246612121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−ii−ii−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−ii−ii
χ51111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−ii−ii
χ81111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiii−ii−i
χ91111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-111-1-111-1-111-1-111-1-1
χ101111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-111-1-1-1-111-1-111-1-111
χ111111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111ii−i−i−i−iiii−i−ii
χ121111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111−i−iiiii−i−i−iii−i
χ131111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111111-111-1-1-1-111-1-111-1-1-1-111
χ141111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111111-111-1-1-1-1-1-111-1-11111-1-1
χ151111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-1-11111ii−i−i−i−iii−iii−i
χ161111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-1-11111−i−iiiii−i−ii−i−ii
χ17222222-1-1-1-122-1-1-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1000000000000
χ18222222-1-1-1-122-1-1-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2111111000000000000
χ19222222-1-1-1-122-1-1-1-1-2-2-1-122-1-1-1-12222-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111222222-1-1-1-1-2-21111-1-1000000000000
χ20222222-1-1-1-122-1-1-1-1-2-2-1-122-1-1-1-12222-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-2-2111122-1-1-1-111000000000000
χ212222-2-2-1-1-1-122-1-1-1-12-21122-1-1-1-12222-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-1-1-1-2211-1-111000000000000
χ222222-2-2-1-1-1-122-1-1-1-12-21122-1-1-1-12222-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-22211112-2-1-111-1-1000000000000
χ232222-2-2-1-1-1-122-1-1-1-1-221122-1-1-1-12222-1-1-1-1-1-1-1-111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-2-2-1-1-1-12-2-1-11111000000000000
χ242222-2-2-1-1-1-122-1-1-1-1-221122-1-1-1-12222-1-1-1-1-1-1-1-111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2221111-2211-1-1-1-1000000000000
χ2522-2-20022-2-22222220000-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i002i2i−2i−2i00000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000
χ2622-2-20022-2-22222220000-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i002i2i−2i−2i0000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000
χ2722-2-20022-2-22222220000-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i00−2i−2i2i2i0000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000
χ2822-2-20022-2-22222220000-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i00−2i−2i2i2i00000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000
χ292-22-22-22-22-2222222002-2222222-2-2-2-2-2-2-2-2-2-2-2-2000022-2-22222-2-2-2-20000000000000000000000002i−2i−2i2i2i−2i2i−2i2i−2i0000002i−2i000000000000
χ302-22-22-22-22-2222222002-2222222-2-2-2-2-2-2-2-2-2-2-2-2000022-2-22222-2-2-2-2000000000000000000000000−2i2i2i−2i−2i2i−2i2i−2i2i000000−2i2i000000000000
χ312-22-22-2-11-1122-1-1-1-100-1122-1-1-1-1-2-2-2-2111111113−33−322-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−32i−2i−2i2i2i−2i−ii−ii00−i3i3−i3i3−ii000000000000
χ322-22-22-2-11-1122-1-1-1-100-1122-1-1-1-1-2-2-2-2111111113−33−322-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−3−2i2i2i−2i−2i2ii−ii−i00i3−i3i3−i3i−i000000000000
χ332-22-22-2-11-1122-1-1-1-100-1122-1-1-1-1-2-2-2-211111111−33−3322-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−333332i−2i−2i2i2i−2i−ii−ii00i3−i3i3−i3−ii000000000000
χ342-22-22-2-11-1122-1-1-1-100-1122-1-1-1-1-2-2-2-211111111−33−3322-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−33333−2i2i2i−2i−2i2ii−ii−i00−i3i3−i3i3i−i000000000000
χ352-22-2-222-22-222222200-22222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-222-2-2-2-222220000000000000000000000002i−2i−2i2i−2i2i2i−2i2i−2i000000−2i2i000000000000
χ362-22-2-222-22-222222200-22222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-222-2-2-2-22222000000000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i0000002i−2i000000000000
χ372-22-2-22-11-1122-1-1-1-1001-122-1-1-1-1-2-2-2-2111111113−3−33-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−333332i−2i−2i2i−2i2i−ii−ii00i3−i3−i3i3i−i000000000000
χ382-22-2-22-11-1122-1-1-1-1001-122-1-1-1-1-2-2-2-2111111113−3−33-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−33333−2i2i2i−2i2i−2ii−ii−i00−i3i3i3−i3−ii000000000000
χ392-22-2-22-11-1122-1-1-1-1001-122-1-1-1-1-2-2-2-211111111−333−3-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−32i−2i−2i2i−2i2i−ii−ii00−i3i3i3−i3i−i000000000000
χ402-22-2-22-11-1122-1-1-1-1001-122-1-1-1-1-2-2-2-211111111−333−3-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−3−2i2i2i−2i2i−2ii−ii−i00i3−i3−i3i3−ii000000000000
χ412-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000000000000022-2-2002-2-22000000002i−2i002i−2i000000
χ422-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000000000000022-2-2002-2-2200000000−2i2i00−2i2i000000
χ432-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000-2-22200-222-2000000002-200-22000000
χ442-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000-2-22200-222-200000000-22002-2000000
χ4544444444441-211-2-244441-211-2-21-21-211-2-211-2-244441-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-2000000000000000000000000000000
χ4644444444441-211-2-2-4-4441-211-2-21-21-211-2-211-2-2-4-4-4-41-21-211-2-211-2-2-1-122-1-122-1-122-1-122-1-122-1-122000000000000000000000000000000
χ474444444444-21-2-2114444-21-2-211-21-21-2-211-2-2114444-21-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000000000000
χ484444444444-21-2-211-4-444-21-2-211-21-21-2-211-2-211-4-4-4-4-21-21-2-211-2-21122-1-122-1-122-1-122-1-122-1-122-1-1000000000000000000000000000000
χ49444444-2-2-2-21-2−1−3i32−1+3i321144-2-21-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-2-2-2-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000000000000
χ50444444-2-2-2-21-2−1−3i32−1+3i3211-4-4-2-21-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i321122221-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
χ51444444-2-2-2-21-2−1+3i32−1−3i321144-2-21-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-2-2-2-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000000000000
χ52444444-2-2-2-21-2−1+3i32−1−3i3211-4-4-2-21-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i321122221-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-1000000000000000000000000000000
χ53444444-2-2-2-2-2111−1−3i32−1+3i3244-2-2-2111−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-2-2-2-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000000000000000000
χ54444444-2-2-2-2-2111−1−3i32−1+3i32-4-4-2-2-2111−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i322222-21-2111−1−3i32−1+3i3211−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i32000000000000000000000000000000
χ55444444-2-2-2-2-2111−1+3i32−1−3i3244-2-2-2111−1+3i32−1−3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2-2-2-2-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32000000000000000000000000000000
χ56444444-2-2-2-2-2111−1+3i32−1−3i32-4-4-2-2-2111−1+3i32−1−3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i322222-21-2111−1+3i32−1−3i3211−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i32000000000000000000000000000000
χ574444-4-444441-211-2-24-4-4-41-211-2-21-21-211-2-211-2-244-4-4-12-12-1-122-1-12211-2-211-2-211-2-2-1-122-1-122-1-122000000000000000000000000000000
χ584444-4-444441-211-2-2-44-4-41-211-2-21-21-211-2-211-2-2-4-444-12-12-1-122-1-122-1-122-1-122-1-12211-2-211-2-211-2-2000000000000000000000000000000
χ594444-4-44444-21-2-2114-4-4-4-21-2-211-21-21-2-211-2-21144-4-42-12-122-1-122-1-1-2-211-2-211-2-21122-1-122-1-122-1-1000000000000000000000000000000
χ604444-4-44444-21-2-211-44-4-4-21-2-211-21-21-2-211-2-211-4-4442-12-122-1-122-1-122-1-122-1-122-1-1-2-211-2-211-2-211000000000000000000000000000000
χ614444-4-4-2-2-2-21-2−1−3i32−1+3i32114-4221-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-2-222-12-121+3i321−3i32-1-11+3i321−3i32-1-111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
χ624444-4-4-2-2-2-21-2−1−3i32−1+3i3211-44221-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i321122-2-2-12-121+3i321−3i32-1-11+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000000000000
χ634444-4-4-2-2-2-21-2−1+3i32−1−3i32114-4221-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-2-222-12-121−3i321+3i32-1-11−3i321+3i32-1-111-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-1000000000000000000000000000000
χ644444-4-4-2-2-2-21-2−1+3i32−1−3i3211-44221-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i321122-2-2-12-121−3i321+3i32-1-11−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-111-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000000000000
χ654444-4-4-2-2-2-2-2111−1−3i32−1+3i324-422-2111−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-2222-12-1-1-11+3i321−3i32-1-11+3i321−3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i32000000000000000000000000000000
χ664444-4-4-2-2-2-2-2111−1−3i32−1+3i32-4422-2111−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i3222-2-22-12-1-1-11+3i321−3i32-1-11+3i321−3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000000000000000000
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χ1088-8-8800-444-4-4222−1+3i3−1−3i300004-2-2-21−3i31+3i34-2-42-2-21−3i31+3i322−1+3i3−1−3i30000000000000000000000000000000000000000000000000000000000000000000000

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