Finite Group Databasebeta

← Group #13138919

Character table — Group #13138919

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order1222344666888812121212242424242424242433666666444436661212121212121212242424242424242424242424242424242266668888121212122424242424242424444444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ911-1-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-11-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i
χ1011-1-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-11-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii
χ1111-1-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii
χ1211-1-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i
χ1311-1-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111111-111-1-1-1-11111-1-1-1-1-1-11111i−i−iii−i−iii−i−iii−i−ii
χ1411-1-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111111-111-1-1-1-11111-1-1-1-1-1-11111−iii−i−iii−i−iii−i−iii−i
χ1511-1-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-1-1111111-1-1-1-1i−i−ii−iii−ii−i−ii−iii−i
χ1611-1-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-1-1111111-1-1-1-1−iii−ii−i−ii−iii−ii−i−ii
χ17222222222222222222222222222-12-12-12-10000-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000000022220000-1-1-1-1
χ18222222222222222222222222222-12-12-12-10000-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000000-2-2-2-200001111
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χ232222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-12-12-120000-1-1-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000000000000022-2-20000-1-1110000
χ242222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-12-12-120000-1-1-1-1-12-1-1-12-1-111-2-2111111-2-211110000000000000000000000-2-222000011-1-10000
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χ2822-2-222-2-2-22000022-2-20000000022-2-222-2-2-2-2222-2-222222-2-2-2-200000000000000002-222-2-20000-2-222000000000000000000000000
χ2922-2-22-22-2-2222-2-2-2-2222222-2-2-2-22-1-212-1-210000-111-1-21112-1-1-122-1-1-1-1-1-1-2-2111111000000000000000000000000002i−2i2i−2i0000−ii−ii
χ3022-2-22-22-2-2222-2-2-2-2222222-2-2-2-22-1-212-1-210000-111-1-21112-1-1-122-1-1-1-1-1-1-2-211111100000000000000000000000000−2i2i−2i2i0000i−ii−i
χ3122-2-22-22-2-2222-2-2-2-2222222-2-2-2-2-121-2-121-20000-111-11-211-12-1-1-1-122-1-1-1-111-2-2111100000000000000000000002i−2i2i−2i0000−ii−ii0000
χ3222-2-22-22-2-2222-2-2-2-2222222-2-2-2-2-121-2-121-20000-111-11-211-12-1-1-1-122-1-1-1-111-2-211110000000000000000000000−2i2i−2i2i0000i−ii−i0000
χ3322-2-22-22-2-22-2-222-2-222-2-2-2-222222-1-212-1-210000-111-1-21112-1-1-1-2-211111122-1-1-1-1-1-1000000000000000000000000002i−2i−2i2i0000−iii−i
χ3422-2-22-22-2-22-2-222-2-222-2-2-2-222222-1-212-1-210000-111-1-21112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000000000−2i2i2i−2i0000i−i−ii
χ3522-2-22-22-2-22-2-222-2-222-2-2-2-22222-121-2-121-20000-111-11-211-12-1-111-2-21111-1-122-1-1-1-100000000000000000000002i−2i−2i2i0000−iii−i0000
χ3622-2-22-22-2-22-2-222-2-222-2-2-2-22222-121-2-121-20000-111-11-211-12-1-111-2-21111-1-122-1-1-1-10000000000000000000000−2i2i2i−2i0000i−i−ii0000
χ372-22-22002-2-22−22−2000022−2−222−2−2222-2-2-2-222i−2i2i−2i22-2-2000000002−22−222−2−22−22−222−2−2000000−i2i2−i2i22i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000000000
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χ412-2-22200-22-22−2−22000022−2−2−2−22222-22-2-22-22i−2i−2i2i2-22-2000000002−22−222−2−2−22−22−2−222000000−i2i2i2−i22i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ422-2-22200-22-22−2−22000022−2−2−2−22222-22-2-22-2−2i2i2i−2i2-22-2000000002−22−222−2−2−22−22−2−222000000i2−i2−i2i2−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ432-2-22200-22-2−222−20000−2−22222−2−222-22-2-22-22i−2i−2i2i2-22-200000000−22−22−2−2222−22−222−2−2000000i2−i2−i2i22i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ442-2-22200-22-2−222−20000−2−22222−2−222-22-2-22-2−2i2i2i−2i2-22-200000000−22−22−2−2222−22−222−2−2000000−i2i2i2−i2−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000000000
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χ464444444444-4-4-4-44444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-200001111-2-211-2-2112222-1-1-1-12222-1-1-1-100000000000000000000000000000000000000
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χ5544-4-44-44-4-4444-4-4-4-4444444-4-4-4-4-2-222-2-22200001-1-1122-1-1-2-211-2-2-2-211112222-1-1-1-100000000000000000000000000000000000000
χ5644-4-44-44-4-44-4-444-4-444-4-4-4-44444-2-222-2-22200001-1-1122-1-1-2-2112222-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000
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χ936-66-6-300-333−3232−323233−3333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000002i−2i2i−2i000000000000000000000000000000−i3i3−i3i3i2−i2i2−i2−ii−ii−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ946-66-6-300-333−3232−323233−3333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ2300000000−2i2i−2i2i000000000000000000000000000000i3−i3i3−i3−i2i2−i2i2i−ii−iζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
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χ986-6-66-3003-3332−32−323233−33−33333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ700000000−2i2i2i−2i000000000000000000000000000000−i3i3i3−i3i2−i2−i2i2i−i−ii−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ996-6-66-3003-3332−32−3232−333333−333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000002i−2i−2i2i000000000000000000000000000000−i3i3i3−i3−i2i2i2−i2−iii−iζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
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χ1026-6-66-3003-33−323232−3233−33−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ700000000−2i2i2i−2i000000000000000000000000000000−i3i3i3−i3−i2i2i2−i2i−i−iiζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ1036-6-66-3003-33−323232−32−333333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000002i−2i−2i2i000000000000000000000000000000−i3i3i3−i3i2−i2−i2i2−iii−i−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ1046-6-66-3003-33−323232−32−333333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ2300000000−2i2i2i−2i000000000000000000000000000000i3−i3−i3i3−i2i2i2−i2i−i−iiζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000

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