Finite Group Databasebeta

← Group #13160987

Character table — Group #13160987

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
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order12222333336666666233334666666666666666666666666666666666666666666666661212121212121212121212121244121212121212121212121212121212124412121212412122244
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
χ511111111111111111-11111-111111111111111111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1111111-1-1-11-11-1
χ611111111111111111-11111-111111111111111111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11
χ711111111111111111-11111-111111111111111111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-11-11
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χ8444-44-4-2-24-2-2-2-24-222-2011-21022-422-2-1-1-1-122-1-111-212-22-2-442-200000-11-112-2-113-3-33003-300000-333-300-330000000000000000000000000000000
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χ8644-44-4-2-2-244-2-2-24-4-440-2-2-240222-4-44222222-4-4-2-2-242-22-22-2-44000002-22-22-2-440000000000000000000000000000000000000000000000000000
χ8744-44-4-2-2-24-2-2-2-2422-20111-20222-42-2-1-1-1-1-1-122111-22-22-22-2-4400000-11-11-112-23-33-3-330000000-33-333-3000000000000000000000000000000000
χ8844-44-4-2-2-24-2-2-2-2422-20111-20222-42-2-1-1-1-1-1-122111-22-22-22-2-4400000-11-11-112-2-33-333-300000003-33-3-33000000000000000000000000000000000
χ8944-4-444-2-2-2-24-2-2-2-2-2-24-2111-44-2-2-222-2-2111111-2111-4-42222224-2-2-2-222-1-1-1-1-1-1-2-2111111-4222222-1-1-1-1-1-10000000000000000000000000000000
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χ9344-4-44-2-24-2-2-2-24-2-2-2-2411-21-4-2-24-2221111-2-21111-212222-4-422-2-24-2-2-1-1-1-122-1-11111-2-21122-422-1-1-1-122-1-10000000000000000000000000000000
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χ9544-4-44-2-2-24-2-2-2-24-2-2-24111-2-4-2-2-2422111111-2-2111-2222222-4-4-2-2-24-2-1-1-1-1-1-122111111-2-2222-42-1-1-1-1-1-1220000000000000000000000000000000
χ9644-4-44-2-2-24-2-2-2-24-2-2-2-4111-24-2-2-2422111111-2-2111-2222222-4-4222-42-1-1-1-1-1-122-1-1-1-1-1-122-2-2-24-2111111-2-20000000000000000000000000000000
χ974-400044444-4-4-4-400-404444000000000000000-4-4-4-40000000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i0000000
χ984-400044444-4-4-4-400-404444000000000000000-4-4-4-4000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i0000000
χ994-40004444-2-4-4-4-4−2i32i320-2-2-2-20000000−2i32i3−2i32i3−2i32i3−2i32i322220000000000000000000000000000000000000000000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ110000000
χ1004-40004444-2-4-4-4-4−2i32i320-2-2-2-20000000−2i32i3−2i32i3−2i32i3−2i32i32222000000000000000000000000000000000000000000000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ110000000
χ1014-40004444-2-4-4-4-42i3−2i320-2-2-2-200000002i3−2i32i3−2i32i3−2i32i3−2i322220000000000000000000000000000000000000000000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ70000000
χ1024-40004444-2-4-4-4-42i3−2i320-2-2-2-200000002i3−2i32i3−2i32i3−2i32i3−2i32222000000000000000000000000000000000000000000000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ70000000
χ1038-80008-4-4-48-844400-808-4-4-4000000000000000-84440000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-80008-4-4-4-4-8444−4i34i340-42220000000−4i34i32i3−2i32i3−2i32i3−2i34-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-80008-4-4-4-4-84444i3−4i340-422200000004i3−4i3−2i32i3−2i32i3−2i32i34-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8000-48-4-484-84400-80-48-4-40000000000000004-8440000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8000-48-4-4-44-844−4i34i3402-42200000002i3−2i3−4i34i32i3−2i32i3−2i3-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8000-48-4-4-44-8444i3−4i3402-4220000000−2i32i34i3−4i3−2i32i3−2i32i3-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8000-4-48-4844-8400-80-4-48-400000000000000044-840000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8000-4-48-4-444-84−4i34i34022-4200000002i3−2i32i3−2i3−4i34i32i3−2i3-2-24-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8000-4-48-4-444-844i3−4i34022-420000000−2i32i3−2i32i34i3−4i3−2i32i3-2-24-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8000-4-4-488444-800-80-4-4-48000000000000000444-80000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8000-4-4-48-4444-8−4i34i340222-400000002i3−2i32i3−2i32i3−2i3−4i34i3-2-2-240000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8000-4-4-48-4444-84i3−4i340222-40000000−2i32i3−2i32i3−2i32i34i3−4i3-2-2-240000000000000000000000000000000000000000000000000000000000000000000000000

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