Finite Group Databasebeta

← Group #13138808

Character table — Group #13138808

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order1222344666888812121212242424242424242433666666366612121212121212122424242424242424242424242424242444448888121212121212121224242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-122-1-1-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ10222222222222222222222222222-122-1-1-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ1122222222222222222222222222-12-1-1222-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ1222222222222222222222222222-12-1-1222-1-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ132222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-1-12-1-1-1-1-12-1-1-12-1-1-2-2-2-21111111111110000000000000000000000002-200-1-1110000
χ142222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-1-12-1-1-1-1-12-1-1-12-1-1-2-2-2-2111111111111000000000000000000000000-220011-1-10000
χ152222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1222-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-211111111000000000000000000000000002-20000-1-111
χ162222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1222-1-1-1-1-12-1-1-12-1-1-11111-2-2-2-21111111100000000000000000000000000-22000011-1-1
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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χ2022-2-2200-22-222−2−200002222−2−2−2−2222-22-2-2-222-2-20000000022−2−222−2−22222−2−2−2−200−2i2ii2i2−i2−i20000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2000000000000
χ2122-2-2200-22-2−2−2220000−2−2−2−22222222-22-2-2-222-2-200000000−2−222−2−222−2−2−2−22222002i−2ii2i2−i2−i200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i2000000000000
χ2222-2-2200-22-2−2−2220000−2−2−2−22222222-22-2-2-222-2-200000000−2−222−2−222−2−2−2−2222200−2i2i−i2−i2i2i20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2000000000000
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χ262-22-2200-2-22−22−220000−2−222−2−22222-22-22-2-22-22-200000000−22−22−22−22−2−222−2−222−2i2i00−i2i2−i2i2−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i2000000000000
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
χ282-2-2222-22-2-22-2-2222-2-222-2-2-2-2222-1-2-211-12-111-11-211-12-1-12-2-22-111-1-1-11111-1-10000000000000000000000000000−i3i3−i3i30000
χ292-2-2222-22-2-22-2-2222-2-222-2-2-2-2222-1-2-211-12-111-11-211-12-1-12-2-22-111-1-1-11111-1-10000000000000000000000000000i3−i3i3−i30000
χ302-2-2222-22-2-22-2-2222-2-222-2-2-2-222-1211-2-22-1-111-1-21112-1-1-1-111-12-2-22-1-11111-1-100000000000000000000000000000000−i3i3−i3i3
χ312-2-2222-22-2-22-2-2222-2-222-2-2-2-222-1211-2-22-1-111-1-21112-1-1-1-111-12-2-22-1-11111-1-100000000000000000000000000000000i3−i3i3−i3
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
χ332-2-2222-22-2-2-222-222-2-2-2-22222-2-22-1-2-211-12-111-11-211-12-1-1-222-21-1-1111-1-1-1-1110000000000000000000000000000−i3i3i3−i30000
χ342-2-2222-22-2-2-222-222-2-2-2-22222-2-22-1-2-211-12-111-11-211-12-1-1-222-21-1-1111-1-1-1-1110000000000000000000000000000i3−i3−i3i30000
χ352-2-2222-22-2-2-222-222-2-2-2-22222-2-2-1211-2-22-1-111-1-21112-1-1-11-1-11-222-211-1-1-1-11100000000000000000000000000000000−i3i3i3−i3
χ362-2-2222-22-2-2-222-222-2-2-2-22222-2-2-1211-2-22-1-111-1-21112-1-1-11-1-11-222-211-1-1-1-11100000000000000000000000000000000i3−i3−i3i3
χ372-2-222-222-2-20000-2-2220000000022-2-2-2-2222-2-222222-2-2-2-2000000000000000000002-2-220000000022-2-2-2-222000000000000
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χ404444444444-4-4-4-44444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-211-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
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χ8166-6-6-3003-33−32−323232−3333−3333−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7000000000000000000000000000000000000002i−2ii2i2−i2−i2i3−i3i3−i3−i−iii−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7000000000000
χ8266-6-6-3003-33−32−323232−3333−3333−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ700000000000000000000000000000000000000−2i2i−i2−i2i2i2−i3i3−i3i3ii−i−iζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ836-66-6-30033-332−3232−3233−33−33333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ230000000000000000000000000000000000002i−2i00−i2i2−i2i2−i−iii−i3i3−i3i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ846-66-6-30033-332−3232−3233−33−33333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000000000000000000000000000000000−2i2i00i2−i2i2−i2ii−i−ii3−i3i3−i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ856-66-6-30033-332−3232−32−333333−333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ70000000000000000000000000000000000002i−2i00−i2i2−i2i2−i−iiii3−i3i3−i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ866-66-6-30033-332−3232−32−333333−333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000000000000000000000000000000000−2i2i00i2−i2i2−i2ii−i−i−i3i3−i3i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ876-66-6-30033-3−3232−323233−33−3333−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ230000000000000000000000000000000000002i−2i00i2−i2i2−i2−i−iii−i3i3−i3i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ886-66-6-30033-3−3232−323233−33−3333−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000000000000000000000000000000000−2i2i00−i2i2−i2i2ii−i−ii3−i3i3−i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ896-66-6-30033-3−3232−3232−333333−33−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ70000000000000000000000000000000000002i−2i00i2−i2i2−i2−i−iiii3−i3i3−i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ906-66-6-30033-3−3232−3232−333333−33−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000000000000000000000000000000000−2i2i00−i2i2−i2i2ii−i−i−i3i3−i3i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ916-6-66-36-6-3336-6-66-3-333-3-33333-3-3000000000000000000000000000000000000000000003−3−33−333−33−3−33−333−3000000000000
χ926-6-66-36-6-3336-6-66-3-333-3-33333-3-300000000000000000000000000000000000000000000−333−33−3−33−333−33−3−33000000000000
χ936-6-66-36-6-333-666-6-3-33333-3-3-3-333000000000000000000000000000000000000000000003−3−33−333−3−333−33−3−33000000000000
χ946-6-66-36-6-333-666-6-3-33333-3-3-3-33300000000000000000000000000000000000000000000−333−33−3−333−3−33−333−3000000000000
χ956-6-66-3-66-333000033-3-333−33−3333−333333−3300000000000000000000000000000000000000002-2-22−333−3−333−3-1-11111-1-1000000000000
χ966-6-66-3-66-333000033-3-333−33−3333−333333−330000000000000000000000000000000000000000-222-23−3−333−3−3311-1-1-1-111000000000000
χ976-6-66-3-66-333000033-3-3−333333−3333−33−333300000000000000000000000000000000000000002-2-223−3−333−3−33-1-11111-1-1000000000000
χ986-6-66-3-66-333000033-3-3−333333−3333−33−33330000000000000000000000000000000000000000-222-2−333−3−333−311-1-1-1-111000000000000

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