Finite Group Databasebeta

← Group #13138805

Character table — Group #13138805

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order1222344666888812121212242424242424242433666666366612121212121212122424242424242424242424242424242444448888121212121212121224242424242424242244666612121212
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
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111
χ9222222222222222222222222222-122-1-12-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-100-1-1
χ10222222222222222222222222222-122-1-12-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-200110011
χ1122222222222222222222222222-12-1-122-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000002020-1-100-1-100
χ1222222222222222222222222222-12-1-122-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000-20-2011001100
χ132222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-12-1-1-12-1-1-1-2-2-2-2111111111111000000000000000000000000020-200-1-10011
χ142222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-12-1-1-12-1-1-1-2-2-2-21111111111110000000000000000000000000-202001100-1-1
χ152222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-21111111100000000000000000000000020-20-1-1001100
χ162222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-211111111000000000000000000000000-20201100-1-100
χ1722222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-2000000000000000022-2-200002222-2-2-2-200000000000000000000
χ1822222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-2220000-2-2-2-2222200000000000000000000
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χ252-22-2200-2-22i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i222-22-22-2-22-22-200000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22i−2i00−22−222i2i−2i−2i0000−2−222−2−222000000000000
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χ272-2-2222-22-2-22-2-2222-2-222-2-2-2-22222-2-2-2-2222-2-22-2-2-2-222222-2-222-2-2222-2-2-2-222000000000000000000000000000000000000
χ282-2-2222-22-2-22-2-2222-2-222-2-2-2-2222-1-2-2112-1-111-1-21112-1-1-12-2-22-111-1-1-11111-1-1000000000000000000000000000000−i3i300−i3i3
χ292-2-2222-22-2-22-2-2222-2-222-2-2-2-2222-1-2-2112-1-111-1-21112-1-1-12-2-22-111-1-1-11111-1-1000000000000000000000000000000i3−i300i3−i3
χ302-2-2222-22-2-22-2-2222-2-222-2-2-2-222-1211-2-2-12-111-11-211-12-1-1-111-12-2-22-1-11111-1-10000000000000000000000000000−i3i300−i3i300
χ312-2-2222-22-2-22-2-2222-2-222-2-2-2-222-1211-2-2-12-111-11-211-12-1-1-111-12-2-22-1-11111-1-10000000000000000000000000000i3−i300i3−i300
χ322-2-2222-22-2-2-222-222-2-2-2-22222-2-222-2-2-2-2222-2-22-2-2-2-22222-222-2-222-2-2-22222-2-2000000000000000000000000000000000000
χ332-2-2222-22-2-2-222-222-2-2-2-22222-2-22-1-2-2112-1-111-1-21112-1-1-1-222-21-1-1111-1-1-1-111000000000000000000000000000000−i3i300i3−i3
χ342-2-2222-22-2-2-222-222-2-2-2-22222-2-22-1-2-2112-1-111-1-21112-1-1-1-222-21-1-1111-1-1-1-111000000000000000000000000000000i3−i300−i3i3
χ352-2-2222-22-2-2-222-222-2-2-2-22222-2-2-1211-2-2-12-111-11-211-12-1-11-1-11-222-211-1-1-1-1110000000000000000000000000000−i3i300i3−i300
χ362-2-2222-22-2-2-222-222-2-2-2-22222-2-2-1211-2-2-12-111-11-211-12-1-11-1-11-222-211-1-1-1-1110000000000000000000000000000i3−i300−i3i300
χ372-2-222-222-2-20000-2-2220000000022-2-2-2-2222-2-222222-2-2-2-2000000000000000000002-2-220000000022-2-2-2-222000000000000
χ382-2-222-222-2-20000-2-2220000000022-2-2-2-2222-2-222222-2-2-2-200000000000000000000-222-200000000-2-22222-2-2000000000000
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χ4444444-4-44440000-4-4-4-400000000-2-2-2-2-2-2-2-2111122-1-122-1-100000000−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000000000
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χ4644-4-4400-44-4−2i2−2i22i22i20000−2i2−2i2−2i2−2i22i22i22i22i2-24-224-42-4-2-22200000000i2i2−i2−i2−2i2−2i22i22i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000000000000
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χ5144-4-4400-44-42i22i2−2i2−2i200002i22i22i22i2−2i2−2i2−2i2−2i2-2-2-22-222211-1-1003i−3i003i−3i−i2−i2i2i2−i2−i2i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000000000000000
χ5244-4-4400-44-42i22i2−2i2−2i200002i22i22i22i2−2i2−2i2−2i2−2i2-2-2-22-222211-1-100−3i3i00−3i3i−i2−i2i2i2−i2−i2i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000000000000
χ534-44-4400-4-44−2i22i2−2i22i20000−2i2−2i22i22i2−2i2−2i22i22i24-2-442-2-42-22-2200000000−2i22i2−2i22i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000000000
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χ8266-6-6-3003-333i23i2−3i2−3i2−3333−3333−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ700000000000000000000000000000000000000−2i2i22−2−2−i3i3−i3i3ii−i−iζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7000000000000
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χ916-6-66-36-6-3336-6-66-3-333-3-33333-3-3000000000000000000000000000000000000000000003−3−33−333−3−333−33−3−33000000000000
χ926-6-66-36-6-3336-6-66-3-333-3-33333-3-300000000000000000000000000000000000000000000−333−33−3−333−3−33−333−3000000000000
χ936-6-66-36-6-333-666-6-3-33333-3-3-3-333000000000000000000000000000000000000000000003−3−33−333−33−3−33−333−3000000000000
χ946-6-66-36-6-333-666-6-3-33333-3-3-3-33300000000000000000000000000000000000000000000−333−33−3−33−333−33−3−33000000000000
χ956-6-66-3-66-333000033-3-333−33−3333−333333−3300000000000000000000000000000000000000002-2-223−3−333−3−33-1-11111-1-1000000000000
χ966-6-66-3-66-333000033-3-333−33−3333−333333−330000000000000000000000000000000000000000-222-2−333−3−333−311-1-1-1-111000000000000
χ976-6-66-3-66-333000033-3-3−333333−3333−33−333300000000000000000000000000000000000000002-2-22−333−3−333−3-1-11111-1-1000000000000
χ986-6-66-3-66-333000033-3-3−333333−3333−33−33330000000000000000000000000000000000000000-222-23−3−333−3−3311-1-1-1-111000000000000

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