Finite Group Databasebeta

← Group #13137395

Character table — Group #13137395

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order1222344444466612121212121212121212121233666666366612121212121212121212121212121212121212121212121288888888242424242424242424242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-122-1-12-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-100-1-1
χ10222222222222222222222222222-122-1-12-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-200110011
χ1122222222222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002020-1-100-1-100
χ1222222222222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-20-2011001100
χ132222222-2-2-2-22222222-2-2-2-2-2-2-2-222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ142222222-2-2-2-22222222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-122-2-2-1-111-2-2111111-1-1-1-11111000000000000000000000000000000−i3i300−i3i3
χ152222222-2-2-2-22222222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-122-2-2-1-111-2-2111111-1-1-1-11111000000000000000000000000000000i3−i300i3−i3
χ162222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-1-11122-2-211-2-21111-1-1-1-111110000000000000000000000000000−i3i300−i3i300
χ172222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-1-11122-2-211-2-21111-1-1-1-111110000000000000000000000000000i3−i300i3−i300
χ1822222-2-222-2-2222-2-2-2-22222-2-2-2-2222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ1922222-2-222-2-2222-2-2-2-22222-2-2-2-22-122-1-12-1-1-1-1-1-2-22211-1-1-2-21111111111-1-1-1-1000000000000000000000000000000−i3i300i3−i3
χ2022222-2-222-2-2222-2-2-2-22222-2-2-2-22-122-1-12-1-1-1-1-1-2-22211-1-1-2-21111111111-1-1-1-1000000000000000000000000000000i3−i300−i3i3
χ2122222-2-222-2-2222-2-2-2-22222-2-2-2-2-12-1-122-12-1-1-1-111-1-1-2-22211-2-211111111-1-1-1-10000000000000000000000000000−i3i300i3−i300
χ2222222-2-222-2-2222-2-2-2-22222-2-2-2-2-12-1-122-12-1-1-1-111-1-1-2-22211-2-211111111-1-1-1-10000000000000000000000000000i3−i300−i3i300
χ2322222-2-2-2-222222-2-2-2-2-2-2-2-222222-122-1-12-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-111111111000000000000000000000000020-200-1-10011
χ2422222-2-2-2-222222-2-2-2-2-2-2-2-222222-122-1-12-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-1111111110000000000000000000000000-202001100-1-1
χ2522222-2-2-2-222222-2-2-2-2-2-2-2-22222-12-1-122-12-1-1-1-11111-2-2-2-2-1-122-1-1-1-11111111100000000000000000000000020-20-1-1001100
χ2622222-2-2-2-222222-2-2-2-2-2-2-2-22222-12-1-122-12-1-1-1-11111-2-2-2-2-1-122-1-1-1-111111111000000000000000000000000-20201100-1-100
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χ332-22-22−2i2i0000-22-2−2i−2i2i2i0000000022-22-22-2-22-22-2−2i2i00−2i2i0000000000−2i−2i2i2i00002−22−2i2−i2i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
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χ404444444-4-4-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-222-2-2222222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
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χ634-4-4440000-44-4-4400000000-4-4444-2-4-4224-2-222-200000000-442-222-2-200000000000000000000000000000000000000000000
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χ676666-3666666-3-3-3-3-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
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χ886-66-6-3−6i6i00003-333i3i−3i−3i−3i33i3−3i33i3−333333−33000000000000000000000000000000000000−22−22−i2i2−i2i2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ896-66-6-3−6i6i00003-333i3i−3i−3i3i3−3i33i3−3i333−33−33330000000000000000000000000000000000002−22−2i2−i2i2−i2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ906-66-6-3−6i6i00003-333i3i−3i−3i3i3−3i33i3−3i333−33−3333000000000000000000000000000000000000−22−22−i2i2−i2i2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ916-6-66-300006-633-333−33−3333−333333−33-3-33300000000000000000000000000000000000000002-2-22−333−33−3−33-1-11111-1-1000000000000
χ926-6-66-300006-633-333−33−3333−333333−33-3-3330000000000000000000000000000000000000000-222-23−3−33−333−311-1-1-1-111000000000000
χ936-6-66-300006-633-3−333333−3333−33−3333-3-33300000000000000000000000000000000000000002-2-223−3−33−333−3-1-11111-1-1000000000000
χ946-6-66-300006-633-3−333333−3333−33−3333-3-3330000000000000000000000000000000000000000-222-2−333−33−3−3311-1-1-1-111000000000000
χ956-6-66-30000-6633-333−33−333333−33−333333-3-30000000000000000000000000000000000002-2-220000-1-11111-1-13−3−33−333−3000000000000
χ966-6-66-30000-6633-333−33−333333−33−333333-3-3000000000000000000000000000000000000-222-2000011-1-1-1-111−333−33−3−33000000000000
χ976-6-66-30000-6633-3−333333−33−333333−3333-3-30000000000000000000000000000000000002-2-220000-1-11111-1-1−333−33−3−33000000000000
χ986-6-66-30000-6633-3−333333−33−333333−3333-3-3000000000000000000000000000000000000-222-2000011-1-1-1-1113−3−33−333−3000000000000

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