Finite Group Databasebeta

← Group #13173356

Character table — Group #13173356

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order122234466633333344666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212222244666644121212121212444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii
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
χ71111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii
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−iii−i−iiiii−i−i
χ911111-1-11111111111-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-11111-1-1-1-11-11-1
χ1011111-1-11111111111-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-1-1-1-1-11111-11-11
χ1111111-1-11111111111-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ1211111-1-11111111111-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ1311111-1-1111111111-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-11-1-1-1-1111111-1-1-1-1-11-11
χ1411111-1-1111111111-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-11-1-1-1-111-1-1-1-111111-11-1
χ1511111-1-1111111111-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1ii−i−i−i−iii−iii−i
χ1611111-1-1111111111-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1−i−iiiii−i−ii−i−ii
χ172222-122-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1000000000000
χ182222-122-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2111111000000000000
χ192222-122-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111222222-1-1-1-1-2-2-1-11111000000000000
χ202222-122-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-2-211112211-1-1-1-1000000000000
χ212222-1-2-2-1-1-122-1-1-1-12-222-1-1-1-122-1-1-1-122-1-1-1-111-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-1-1-12-211-1-111000000000000
χ222222-1-2-2-1-1-122-1-1-1-12-222-1-1-1-122-1-1-1-122-1-1-1-111-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2221111-22-1-111-1-1000000000000
χ232222-1-2-2-1-1-122-1-1-1-1-2222-1-1-1-122-1-1-1-122-1-1-1-11111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-221111-1-1000000000000
χ242222-1-2-2-1-1-122-1-1-1-1-2222-1-1-1-122-1-1-1-122-1-1-1-11111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-22211112-2-1-1-1-111000000000000
χ2522-2-22002-2-222222200222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002-22-20022-2-2000000002-22-200000000
χ2622-2-22002-2-222222200222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002-22-20022-2-200000000-22-2200000000
χ2722-2-22002-2-222222200222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000-22-2200-2-222000000002i−2i−2i2i00000000
χ2822-2-22002-2-222222200222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000-22-2200-2-22200000000−2i2i2i−2i00000000
χ292-22-222-2-22-222222200-2-2-2-2-2-2222222-2-2-2-2-2-22-2000022-2-22222-2-2-2-200000000000000000000000022-2-22-22-22-2002-20000000000000000
χ302-22-222-2-22-222222200-2-2-2-2-2-2222222-2-2-2-2-2-22-2000022-2-22222-2-2-2-2000000000000000000000000-2-222-22-22-2200-220000000000000000
χ312-22-22-22-22-222222200-2-2-2-2-2-2222222-2-2-2-2-2-2-220000-2-222-2-2-2-2222200000000000000000000000022-2-2-222-22-200-220000000000000000
χ322-22-22-22-22-222222200-2-2-2-2-2-2222222-2-2-2-2-2-2-220000-2-222-2-2-2-22222000000000000000000000000-2-2222-2-22-22002-20000000000000000
χ332-22-2-12-21-1122-1-1-1-100-2-2111122-1-1-1-1-2-21111-113−33−322-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−322-2-22-2-11-1100-113−33−3000000000000
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χ352-22-2-12-21-1122-1-1-1-100-2-2111122-1-1-1-1-2-21111-11−33−3322-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−3333322-2-22-2-11-1100-11−33−33000000000000
χ362-22-2-12-21-1122-1-1-1-100-2-2111122-1-1-1-1-2-21111-11−33−3322-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−33333-2-222-221-11-1001-13−33−3000000000000
χ372-22-2-1-221-1122-1-1-1-100-2-2111122-1-1-1-1-2-211111-13−3−33-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−3333322-2-2-22-11-11001-13−3−33000000000000
χ382-22-2-1-221-1122-1-1-1-100-2-2111122-1-1-1-1-2-211111-13−3−33-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−33333-2-2222-21-11-100-11−333−3000000000000
χ392-22-2-1-221-1122-1-1-1-100-2-2111122-1-1-1-1-2-211111-1−333−3-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−322-2-2-22-11-11001-1−333−3000000000000
χ402-22-2-1-221-1122-1-1-1-100-2-2111122-1-1-1-1-2-211111-1−333−3-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−3-2-2222-21-11-100-113−3−33000000000000
χ412-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000002-2-22002-2-220000000000002-22-20000
χ422-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000002-2-22002-2-22000000000000-22-220000
χ432-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000-222-200-222-20000000000002i−2i−2i2i0000
χ442-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000-222-200-222-2000000000000−2i2i2i−2i0000
χ4544444444441-211-2-2441-211-2-21-211-2-21-211-2-24444441-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-2000000000000000000000000000000
χ4644444444441-211-2-2-4-41-211-2-21-211-2-21-211-2-244-4-4-4-41-21-211-2-211-2-2-1-122-1-122-1-122-1-122-1-122-1-122000000000000000000000000000000
χ474444444444-21-2-21144-21-2-211-21-2-211-21-2-211444444-21-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000000000000
χ484444444444-21-2-211-4-4-21-2-211-21-2-211-21-2-21144-4-4-4-4-21-21-2-211-2-21122-1-122-1-122-1-122-1-122-1-122-1-1000000000000000000000000000000
χ4944444-4-44441-211-2-24-41-211-2-21-211-2-21-211-2-2-4-444-4-4-12-12-1-122-1-12211-2-211-2-211-2-2-1-122-1-122-1-122000000000000000000000000000000
χ5044444-4-44441-211-2-2-441-211-2-21-211-2-21-211-2-2-4-4-4-444-12-12-1-122-1-122-1-122-1-122-1-12211-2-211-2-211-2-2000000000000000000000000000000
χ5144444-4-4444-21-2-2114-4-21-2-211-21-2-211-21-2-211-4-444-4-42-12-122-1-122-1-1-2-211-2-211-2-21122-1-122-1-122-1-1000000000000000000000000000000
χ5244444-4-4444-21-2-211-44-21-2-211-21-2-211-21-2-211-4-4-4-4442-12-122-1-122-1-122-1-122-1-122-1-1-2-211-2-211-2-211000000000000000000000000000000
χ534444-244-2-2-21-2−1−3i32−1+3i3211441-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-2-2-2-2-2-21-21-2−1−3i32−1+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
χ544444-244-2-2-21-2−1−3i32−1+3i3211-4-41-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-2-222221-21-2−1−3i32−1+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
χ554444-244-2-2-21-2−1+3i32−1−3i3211441-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-2-2-2-2-2-21-21-2−1+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
χ564444-244-2-2-21-2−1+3i32−1−3i3211-4-41-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-2-222221-21-2−1+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
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χ584444-244-2-2-2-2111−1−3i32−1+3i32-4-4-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-22222-21-2111−1−3i32−1+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
χ594444-244-2-2-2-2111−1+3i32−1−3i3244-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-2-2-2-2-2-21-2111−1+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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χ684444-2-4-4-2-2-2-2111−1+3i32−1−3i32-44-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i322222-2-22-12-1-1-11−3i321+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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χ9988-8-8-400-4442-4−1−3i3−1+3i322002-4−1−3i3−1+3i322-241+3i31−3i3-2-2-241+3i31−3i3-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-400-4442-4−1+3i3−1−3i322002-4−1+3i3−1−3i322-241−3i31+3i3-2-2-241−3i31+3i3-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-400-444-4222−1−3i3−1+3i300-4222−1−3i3−1+3i34-2-2-21+3i31−3i34-2-2-21+3i31−3i3000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-400-444-4222−1+3i3−1−3i300-4222−1+3i3−1−3i34-2-2-21−3i31+3i34-2-2-21−3i31+3i3000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88800-8-882-422-4-400-24-2-244-24-2-2442-422-4-4000000000000000000000000000000000000000000000000000000000000000000000000
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χ1058-8-88-40044-42-4−1−3i3−1+3i32200-241+3i31−3i3-2-2-241+3i31−3i3-2-22-4−1−3i3−1+3i322000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-40044-42-4−1+3i3−1−3i32200-241−3i31+3i3-2-2-241−3i31+3i3-2-22-4−1+3i3−1−3i322000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-40044-4-4222−1−3i3−1+3i3004-2-2-21+3i31−3i34-2-2-21+3i31−3i3-4222−1−3i3−1+3i3000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-40044-4-4222−1+3i3−1−3i3004-2-2-21−3i31+3i34-2-2-21−3i31+3i3-4222−1+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000

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