Finite Group Databasebeta

← Group #13161405

Character table — Group #13161405

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11222222222222222444444444444444444444444444444448888888888888888888888888888888888242424242424242424242424242424242424363636363636727272108108108108
order1223333344666661212233334666666666121212121212121212121212121212121266666666666666666121212121212121212121212121212121248121212121212121224242424242424244412121212824242224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-11111-111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1
χ611111111111111111-11111-111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ711111111111111111-11111-111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1-111
χ811111111111111111-11111-111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-1
χ922222222-2-222222-2-2022220222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000022220000000000000-2-2-2-2000000000000000000000000000000000002-200
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χ112222222-122-12222-1-12-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12-1-10000
χ122222222-122-12222-1-12-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21111-2110000
χ132222222-122-12222-1-1-2-1-1-1-1-22222-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-21-1-1-1-1111111111-2-2-2-2-1-1-1-11111111100000000000000000022-1-1-1-1-2110000
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χ3122-2222222-222222-2-222222-2-2-2-2-22222-22-2-2-2-2-2-2-2-2-2-2-2-2222222222-2-2-2-222222222-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000
χ3222-2222222-222222-2-2-222222-2-2-2-22222-22-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222220000000000000000000000000000000
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χ3622-22222-12-2-12222112-1-1-1-1-2-2-2-2-2-1-1-1-11-1-2-2-2-21111111122222222-11111-1-1-1-1-1-1-1-11-2-2-2-2-1-1-1-11111111100000000000000000000−3−3330−330000
χ3722-22222-12-2-1222211-2-1-1-1-12-2-2-2-2-1-1-1-11-1-2-2-2-2111111112222-2-2-2-21111111111111-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000033−3−30−330000
χ3822-22222-12-2-1222211-2-1-1-1-12-2-2-2-2-1-1-1-11-1-2-2-2-2111111112222-2-2-2-21111111111111-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000−3−33303−30000
χ3922-22-1-1-122-222-1-1-1-2-222-1-1-1-2-21112-1-1-1-22-2111-2-21111112-1-1-12-1-1-12-211122-1-1-1-1-1-1-2-21112-1-1-1-2-21111110000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i30000000000000
χ4022-22-1-1-122-222-1-1-1-2-222-1-1-1-2-21112-1-1-1-22-2111-2-21111112-1-1-12-1-1-12-211122-1-1-1-1-1-1-2-21112-1-1-1-2-21111110000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i30000000000000
χ4122-22-1-1-122-222-1-1-1-2-2-22-1-1-12-21112-1-1-1-22-2111-2-21111112-1-1-1-2111-2-2111-2-211111122-1-1-12-1-1-122-1-1-1-1-1-10000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i30000000000000
χ4222-22-1-1-122-222-1-1-1-2-2-22-1-1-12-21112-1-1-1-22-2111-2-21111112-1-1-1-2111-2-2111-2-211111122-1-1-12-1-1-122-1-1-1-1-1-10000i3−i3i3−i3i3−i300−i3i3−i3i3−i3i30000000000000
χ4322-2-12-1-122-22-12-1-1-2-22-12-1-1-21-211-12-1-1-221-21111-2-21111-12-1-1-12-1-121-211-1-122-1-1-1-1-21-211-12-1-111-2-2111100−i3i300−i3i3i3−i3−i3i300−i3i3i3−i30000000000000
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χ7644-44444-2-44-24444-2-20-2-2-2-20-4-4-4-4-2-2-2-2224444-2-2-2-2-2-2-2-2-4-4-4-400000222200000000000002222000000000000000000000000000000000000000
χ7744-44-2-2-24-4444-2-2-24404-2-2-20-42224-2-2-2-4-44-2-2-244-2-2-2-2-2-2-422200000-42220000000000000-4222000000000000000000000000000000000000000
χ7844-44-2-2-2-24-4-24-2-2-2224-2111-4-4222-21112-2-422222-1-1-1-1-1-14-2-2-24-2-2-2-22-1-1-1-2-21111112-4222-211122-1-1-1-1-1-10000000000000000000000000000000
χ7944-44-2-2-2-24-4-24-2-2-222-4-21114-4222-21112-2-422222-1-1-1-1-1-14-2-2-2-422222-1-1-122-1-1-1-1-1-1-24-2-2-2-2111-2-21111110000000000000000000000000000000
χ8044-44-2-2-2-2-44-24-2-2-2-2-20-21110-4222-2111224-2-2-2-2-2111111-4222000002-1-1-1003-33-33-3000002-1-1-100-33-33-330000000000000000000000000000000
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χ8244-4-24-2-24-444-24-2-2440-24-2-202-422-24-2-2-4-4-24-2-2-2-244-2-2-2-22-422000002-42200000000000002-422000000000000000000000000000000000000000
χ8344-4-24-2-2-24-4-2-24-2-22241-211-42-4221-2112-22-422-1-122-1-1-1-1-24-2-2-24-2-2-2-12-1-111-2-2111122-4221-211-1-122-1-1-1-10000000000000000000000000000000
χ8444-4-24-2-2-24-4-2-24-2-222-41-21142-4221-2112-22-422-1-122-1-1-1-1-24-2-22-4222-12-1-1-1-122-1-1-1-1-2-24-2-21-21111-2-211110000000000000000000000000000000
χ8544-4-24-2-2-2-44-2-24-2-2-2-201-21102-4221-21122-24-2-211-2-211112-42200000-12-1-13-3003-3-3300000-12-1-1-3300-333-30000000000000000000000000000000
χ8644-4-24-2-2-2-44-2-24-2-2-2-201-21102-4221-21122-24-2-211-2-211112-42200000-12-1-1-3300-333-300000-12-1-13-3003-3-330000000000000000000000000000000
χ8744-4-2-24-24-444-2-24-2440-2-24-2022-42-2-24-2-4-4-2-24-2-2-2-2-244-2-222-420000022-42000000000000022-42000000000000000000000000000000000000000
χ8844-4-2-24-2-24-4-2-2-24-222411-21-422-4211-212-222-42-1-1-1-122-1-1-2-24-2-2-24-2-2-1-12-11111-2-211222-4211-21-1-1-1-122-1-10000000000000000000000000000000
χ8944-4-2-24-2-24-4-2-2-24-222-411-21422-4211-212-222-42-1-1-1-122-1-1-2-24-222-422-1-12-1-1-1-1-122-1-1-2-2-24-211-211111-2-2110000000000000000000000000000000
χ9044-4-2-24-2-2-44-2-2-24-2-2-2011-21022-4211-2122-2-24-21111-2-21122-4200000-1-12-13-3-33003-300000-1-12-1-333-300-330000000000000000000000000000000
χ9144-4-2-24-2-2-44-2-2-24-2-2-2011-21022-4211-2122-2-24-21111-2-21122-4200000-1-12-1-333-300-3300000-1-12-13-3-33003-30000000000000000000000000000000
χ9244-4-2-2-244-444-2-2-24440-2-2-240222-4-2-2-24-4-4-2-2-24-2-2-2-2-2-244222-400000222-40000000000000222-4000000000000000000000000000000000000000
χ9344-4-2-2-24-24-4-2-2-2-24224111-2-4222-4111-22-2222-4-1-1-1-1-1-122-2-2-24-2-2-24-2-1-1-12111111-2-22222-4111-2-1-1-1-1-1-1220000000000000000000000000000000
χ9444-4-2-2-24-24-4-2-2-2-2422-4111-24222-4111-22-2222-4-1-1-1-1-1-122-2-2-24222-42-1-1-12-1-1-1-1-1-122-2-2-2-24111-2111111-2-20000000000000000000000000000000
χ9544-4-2-2-24-2-44-2-2-2-24-2-20111-20222-4111-222-2-2-24111111-2-2222-400000-1-1-123-33-3-330000000-1-1-12-33-333-3000000000000000000000000000000000
χ9644-4-2-2-24-2-44-2-2-2-24-2-20111-20222-4111-222-2-2-24111111-2-2222-400000-1-1-12-33-333-30000000-1-1-123-33-3-33000000000000000000000000000000000
χ974-404444400-4-4-4-4-4000444400000-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i0000000
χ984-404444400-4-4-4-4-4000444400000-4-4-4-40000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i0000000
χ994-404444-2002-4-4-4-423−230-2-2-2-200000222200000023−2323−2323−2323−23000000000000000000000000000000000000000000000000000000002i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000
χ1004-404444-2002-4-4-4-423−230-2-2-2-200000222200000023−2323−2323−2323−2300000000000000000000000000000000000000000000000000000000−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000
χ1014-404444-2002-4-4-4-4−23230-2-2-2-2000002222000000−2323−2323−2323−2323000000000000000000000000000000000000000000000000000000002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000
χ1024-404444-2002-4-4-4-4−23230-2-2-2-2000002222000000−2323−2323−2323−232300000000000000000000000000000000000000000000000000000000−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000
χ1038-808-4-4-4800-8-84440008-4-4-400000-844400000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-808-4-4-4-4004-844443−430-4222000004-2-2-200000043−43−2323−2323−2323000000000000000000000000000000000000000000000000000000000000000000000
χ1058-808-4-4-4-4004-8444−43430-4222000004-2-2-2000000−434323−2323−2323−23000000000000000000000000000000000000000000000000000000000000000000000
χ1068-80-48-4-4800-84-844000-48-4-4000004-84400000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-80-48-4-4-40044-84443−4302-42200000-24-2-2000000−232343−43−2323−2323000000000000000000000000000000000000000000000000000000000000000000000
χ1088-80-48-4-4-40044-844−434302-42200000-24-2-200000023−23−434323−2323−23000000000000000000000000000000000000000000000000000000000000000000000
χ1098-80-4-48-4800-844-84000-4-48-40000044-8400000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-80-4-48-4-400444-8443−43022-4200000-2-24-2000000−2323−232343−43−2323000000000000000000000000000000000000000000000000000000000000000000000
χ1118-80-4-48-4-400444-84−4343022-4200000-2-24-200000023−2323−23−434323−23000000000000000000000000000000000000000000000000000000000000000000000
χ1128-80-4-4-48800-8444-8000-4-4-4800000444-800000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-80-4-4-48-4004444-843−430222-400000-2-2-24000000−2323−2323−232343−43000000000000000000000000000000000000000000000000000000000000000000000
χ1148-80-4-4-48-4004444-8−43430222-400000-2-2-2400000023−2323−2323−23−4343000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.