Finite Group Databasebeta

← Group #13173343

Character table — Group #13173343

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order12222236663333334466666666666666666666121212126666666666661212121212121212121212121212121212121212121212122222226666446612121212444444444444
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
χ51111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−ii−ii
χ81111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiii−ii−i
χ91111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-111-1-111-1-111-1-1
χ101111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-1-1-111-1-111-1-111
χ111111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ121111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ131111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-11-1-1-1-11111-1-111-1-1-1-111
χ141111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-11-1-1-1-111-1-111-1-11111-1-1
χ151111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1ii−i−i−i−iii−iii−i
χ161111-1-11111111111-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1−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
χ19222222-1-1-1-122-1-1-1-1-2-2-1-122-1-1-1-12222-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111222222-1-1-1-1-2-2-1-11111000000000000
χ20222222-1-1-1-122-1-1-1-1-2-2-1-122-1-1-1-12222-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-2-211112211-1-1-1-1000000000000
χ212222-2-2-1-1-1-122-1-1-1-12-21122-1-1-1-12222-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-1-1-12-211-1-111000000000000
χ222222-2-2-1-1-1-122-1-1-1-12-21122-1-1-1-12222-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2221111-22-1-111-1-1000000000000
χ232222-2-2-1-1-1-122-1-1-1-1-221122-1-1-1-12222-1-1-1-1-1-1-1-111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-221111-1-1000000000000
χ242222-2-2-1-1-1-122-1-1-1-1-221122-1-1-1-12222-1-1-1-1-1-1-1-111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-22211112-2-1-1-1-111000000000000
χ2522-2-22-222-2-2222222002-2222222-2-2-2-2-2-2-2-2-2-2-2-2000022-2-22222-2-2-2-200000000000000000000000022-2-22-222-2-2002-20000000000000000
χ2622-2-22-222-2-2222222002-2222222-2-2-2-2-2-2-2-2-2-2-2-2000022-2-22222-2-2-2-2000000000000000000000000-2-222-22-2-22200-220000000000000000
χ2722-2-22-2-1-11122-1-1-1-100-1122-1-1-1-1-2-2-2-2111111113−33−322-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−322-2-22-2-1-11100-113−33−3000000000000
χ2822-2-22-2-1-11122-1-1-1-100-1122-1-1-1-1-2-2-2-2111111113−33−322-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−3-2-222-2211-1-1001-1−33−33000000000000
χ2922-2-22-2-1-11122-1-1-1-100-1122-1-1-1-1-2-2-2-211111111−33−3322-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−3333322-2-22-2-1-11100-11−33−33000000000000
χ3022-2-22-2-1-11122-1-1-1-100-1122-1-1-1-1-2-2-2-211111111−33−3322-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−33333-2-222-2211-1-1001-13−33−3000000000000
χ3122-2-2-2222-2-222222200-22222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-222-2-2-2-2222200000000000000000000000022-2-2-2222-2-200-220000000000000000
χ3222-2-2-2222-2-222222200-22222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-222-2-2-2-22222000000000000000000000000-2-2222-2-2-222002-20000000000000000
χ3322-2-2-22-1-11122-1-1-1-1001-122-1-1-1-1-2-2-2-2111111113−3−33-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−3333322-2-2-22-1-111001-13−3−33000000000000
χ3422-2-2-22-1-11122-1-1-1-1001-122-1-1-1-1-2-2-2-2111111113−3−33-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−33333-2-2222-211-1-100-11−333−3000000000000
χ3522-2-2-22-1-11122-1-1-1-1001-122-1-1-1-1-2-2-2-211111111−333−3-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−322-2-2-22-1-111001-1−333−3000000000000
χ3622-2-2-22-1-11122-1-1-1-1001-122-1-1-1-1-2-2-2-211111111−333−3-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−3-2-2222-211-1-100-113−3−33000000000000
χ372-22-2002-22-22222220000-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002-22-2002-22-200000000002i−2i002i−2i0000
χ382-22-2002-22-22222220000-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002-22-2002-22-20000000000−2i2i00−2i2i0000
χ392-22-2002-22-22222220000-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000-22-2200-22-2200000000002-200-220000
χ402-22-2002-22-22222220000-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000-22-2200-22-220000000000-22002-20000
χ412-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000000000002-2-22002-2-22000000002-2002-2000000
χ422-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000000000002-2-22002-2-2200000000-2200-22000000
χ432-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000-222-200-222-2000000002i−2i00−2i2i000000
χ442-2-22002-2-222222220000-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000-222-200-222-200000000−2i2i002i−2i000000
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
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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
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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
χ674444-4-4-2-2-2-2-2111−1+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
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χ998-88-800-44-442-4−1−3i3−1+3i3220000-241+3i31−3i3-2-22-4-24−1−3i3−1+3i3221+3i31−3i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
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χ1018-88-800-44-44-4222−1−3i3−1+3i300004-2-2-21+3i31−3i3-424-222−1−3i3−1+3i3-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-800-44-44-4222−1+3i3−1−3i300004-2-2-21−3i31+3i3-424-222−1+3i3−1−3i3-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000
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χ1058-8-8800-444-42-4−1−3i3−1+3i3220000-241+3i31−3i3-2-2-242-41+3i31−3i3-2-2−1−3i3−1+3i3220000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-8800-444-42-4−1+3i3−1−3i3220000-241−3i31+3i3-2-2-242-41−3i31+3i3-2-2−1+3i3−1−3i3220000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-8800-444-4-4222−1−3i3−1+3i300004-2-2-21+3i31−3i34-2-42-2-21+3i31−3i322−1−3i3−1+3i30000000000000000000000000000000000000000000000000000000000000000000000
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 12 (ζ12 = 1); i = ζ3.