Finite Group Databasebeta

← Group #13147072

Character table — Group #13147072

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11111111111122222266666666666666121212121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636727272727272
order12223366666644121212123446661212121212121212266666666121212121212333666666666121212121212121212121212888824242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ4111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ522222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ6222222222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ7222222222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-122-1-1-12-1-1-1-1-12222-1-1-1-1000000000000000000
χ8222222222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-12-1-1-1-1-1-1-1-12222000000000000000000
χ9222222222222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000
χ10222222222222-2-2-2-2-2-2-122-1-1-111112222-2-2-2111111-1-1-1-1-1-12-1-122-1-1-1-12-1-1-2-2-2-211111111000000000000000000
χ11222222222222-2-2-2-2-2-2-122-1-1-111112222-2-2-2111111-1-1-1-1-1-1-12-1-1-122-1-1-12-11111-2-2-2-21111000000000000000000
χ12222222222222-2-2-2-2-2-2-122-1-1-111112222-2-2-2111111-1-1-1-1-1-1-1-12-1-1-1-122-1-1211111111-2-2-2-2000000000000000000
χ132-22-222-2-222-2-22i−2i2i2i−2i−2i2002-2-22i2i−2i−2i0000000000000000000-1-1-11-11-11-1111ii−i−iii−i−iii−i−i−i2i22−2−i2−i2i2i222−2−2000000
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χ172-2-2222-2-2-2-22200000022-2-2-22000022-2-2000000000222-2-2-2222-2-2-2-2-2-2222000000000000000000000000000000
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χ202-2-2222-2-2-2-222000000-12-211-1−i3i3−i3i322-2-2000−i3−i3−i3i3i3i3-1-1-11112-1-1-2-211112-1-10000−i3i3−i3i3i3−i3i3−i3000000000000000000
χ212-2-2222-2-2-2-222000000-12-211-1−i3i3−i3i322-2-2000−i3−i3−i3i3i3i3-1-1-1111-12-111-2-211-12-1i3−i3i3−i30000−i3i3−i3i3000000000000000000
χ222-2-2222-2-2-2-222000000-12-211-1−i3i3−i3i322-2-2000−i3−i3−i3i3i3i3-1-1-1111-1-121111-2-2-1-12−i3i3−i3i3i3−i3i3−i30000000000000000000000
χ232-2-2222-2-2-2-222000000-12-211-1i3−i3i3−i322-2-2000i3i3i3−i3−i3−i3-1-1-11112-1-1-2-211112-1-10000i3−i3i3−i3−i3i3−i3i3000000000000000000
χ242-2-2222-2-2-2-222000000-12-211-1i3−i3i3−i322-2-2000i3i3i3−i3−i3−i3-1-1-1111-12-111-2-211-12-1−i3i3−i3i30000i3−i3i3−i3000000000000000000
χ252-2-2222-2-2-2-222000000-12-211-1i3−i3i3−i322-2-2000i3i3i3−i3−i3−i3-1-1-1111-1-121111-2-2-1-12i3−i3i3−i3−i3i3−i3i30000000000000000000000
χ263333333333333333333-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000111111111111-1-1-1-1-1-1
χ273333333333333333333-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1111111
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χ29333333333333-3-3-3-3-3-33-1-1333-3-3-3-3-1-1-1-1111111111-1-1-1-1-1-1000000000000000000000000-1-111-1-1-1-111111-111-1-1
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χ313333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320330000000−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320-1-100000001+i321−i321+i321−i32-11+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i30000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320-1-100000001+i321−i321+i321−i32-11+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
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χ353333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320330000000−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ363333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-1-100000001+i321−i321+i321−i321−1−i32−1+i32-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i300000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-111+i321−i32−1−i32−1+i32
χ373333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-1-100000001+i321−i321+i321−i321−1−i32−1+i32-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ383333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320330000000−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i320000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ393333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320330000000−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ403333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320-1-100000001−i321+i321−i321+i32-11−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i30000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ413333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320-1-100000001−i321+i321−i321+i32-11−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ423333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320330000000−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3200000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1−1+i32−1−i321−i321+i32
χ433333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320330000000−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ443333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320-1-100000001−i321+i321−i321+i321−1+i32−1−i32-21−i31+i3-21−i31+i32−1+i3−1−i32−1+i3−1−i300000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-111−i321+i32−1+i32−1−i32
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χ676666−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i366−3+3i3−3−3i3−3+3i3−3−3i30-2-200000001−i31+i31−i31+i3-21−i31+i3-21−i31+i3-21−i31+i3-21−i31+i3-21−i31+i3000000000000000000000000000000000000000000
χ686666−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3-6-63−3i33+3i33−3i33+3i30-2-200000001−i31+i31−i31+i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i3000000000000000000000000000000000000000000
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χ736-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i36i−6i6ζ146ζ22−6ζ14−6ζ2200000000000000000000000000000000000000000000000000000−i2i22−2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000
χ746-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i36i−6i6ζ146ζ22−6ζ14−6ζ2200000000000000000000000000000000000000000000000000000i2−i2−22−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000
χ756-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i3−6i6i−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000000000000000000000000−i2i2−22ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000
χ766-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i3−6i6i−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000000000000000000000000i2−i22−2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000
χ776-6-6666-6-6-6-6660000006-22-6-660000-2-222000000000-2-2-2222000000000000000000000000000000000000000000
χ786-6-6666-6-6-6-666000000-3-2233-3−3i33i3−3i33i3-2-222000i3i3i3−i3−i3−i3111-1-1-1000000000000000000000000000000000000000000
χ796-6-6666-6-6-6-666000000-3-2233-33i3−3i33i3−3i3-2-222000−i3−i3−i3i3i3i3111-1-1-1000000000000000000000000000000000000000000
χ806-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i300000006-60000000−3−3i3−3+3i33+3i33−3i3000000000000000000000000000000000000000000000000000000000
χ816-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000-2200000001+i31−i3−1−i3−1+i30000000004−2−2i3−2+2i3-42+2i32−2i3000000000000000000000000000000000000000000
χ826-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000-2200000001+i31−i3−1−i3−1+i3000−2i3−3+i33+i32i33−i3−3−i3-21+i31−i32−1−i3−1+i3000000000000000000000000000000000000000000
χ836-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000-2200000001+i31−i3−1−i3−1+i30002i33−i3−3−i3−2i3−3+i33+i3-21+i31−i32−1−i3−1+i3000000000000000000000000000000000000000000
χ846-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i300000006-60000000−3+3i3−3−3i33−3i33+3i3000000000000000000000000000000000000000000000000000000000
χ856-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000-2200000001−i31+i3−1+i3−1−i30000000004−2+2i3−2−2i3-42−2i32+2i3000000000000000000000000000000000000000000
χ866-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000-2200000001−i31+i3−1+i3−1−i3000−2i33+i3−3+i32i3−3−i33−i3-21−i31+i32−1+i3−1−i3000000000000000000000000000000000000000000
χ876-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000-2200000001−i31+i3−1+i3−1−i30002i3−3−i33−i3−2i33+i3−3+i3-21−i31+i32−1+i3−1−i3000000000000000000000000000000000000000000
χ881212-12-12−6−6i3−6+6i3−6−6i3−6+6i36+6i36−6i36+6i36−6i300000000000000000000000000000000000000000000000000000000000000000000000000000
χ891212-12-12−6+6i3−6−6i3−6+6i3−6−6i36−6i36+6i36−6i36+6i300000000000000000000000000000000000000000000000000000000000000000000000000000

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