Finite Group Databasebeta

← Group #72270254

Character table — Group #72270254

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222222222224444444444444444448888888888881616161616161616161616161616161616161616161616161616161616161616161616162424242424242424484848484848484848484848
order12222344446664444668888888812121212121212122424242424242424224444666688121212121212121216161616242424244848484848484848244488882244448816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111
χ51111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111
χ71111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1
χ101111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111
χ111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11-1111-1-1-1-111
χ121111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1111-11-1-1-11111-1-1
χ131111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11-11-1-1-111-1-111
χ141111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11-1111-1-111-1-1
χ151111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ161111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111
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χ2122222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-1-1-1-1-2-21111-1-1-1-1-2-2-2-211111111111100000000000000000000
χ2322222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2111122-1-1-1-11111-2-2-2-2-1-1-1-11111111100000000000000000000
χ2422222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-21111111122221111-1-1-1-1-1-1-1-100000000000000000000
χ2522222-12222-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-1-1-11111-1-11111-1-12222-2-2-1-1-1-1-2-2-1-1-1-1111122-2-21111-1-1-1-1111100000000000000000000
χ2622222-12222-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-1-1-11111-1-11111-1-122-2-2-2-2-1-1-1-12211111111-2-222-1-1-1-11111-1-1-1-100000000000000000000
χ2722222-12222-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-1-1-11111-1-11111-1-1-2-222221111-2-2-1-1-1-1-1-1-1-1-2-22211111111-1-1-1-100000000000000000000
χ2822222-12222-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-1-1-11111-1-11111-1-1-2-2-2-2221111221111-1-1-1-122-2-2-1-1-1-1-1-1-1-1111100000000000000000000
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χ30222-2-22-222-22-2-22i2i−2i−2i2-22i2i−2i−2i2-22-2-22-222i2i−2i−2i2-22i2i−2i−2i2-2000000000000000000000000000000000000000000000-20200−2i2i0000
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χ32222-2-22-222-22-2-22i2i−2i−2i2-2−2i−2i2i2i-22-22-22-222i2i−2i−2i-22−2i−2i2i2i-2200−2i2i000000-22−2i−2i2i2i00000000-2-2220000000000000000000000000000
χ33222-2-22-222-22-2-2−2i−2i2i2i2-22i2i−2i−2i-22-22-22-22−2i−2i2i2i-222i2i−2i−2i-22002i−2i000000-222i2i−2i−2i00000000-2-2220000000000000000000000000000
χ34222-2-22-222-22-2-2−2i−2i2i2i2-22i2i−2i−2i-22-22-22-22−2i−2i2i2i-222i2i−2i−2i-2200−2i2i0000002-2−2i−2i2i2i0000000022-2-20000000000000000000000000000
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χ39222-2-2-1-222-2-1112i2i−2i−2i-11−2i−2i2i2i-22-221-11-1−i−iii1-1ii−i−i1-100−2i2i00−i3−i3i3i3-22ii−i−i33−3−3000011-1-1−3−333i3i3−i3−i300000000000000000000
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χ41222-2-2-1-222-2-111−2i−2i2i2i-112i2i−2i−2i-22-221-11-1ii−i−i1-1−i−iii1-1002i−2i00−i3−i3i3i3-22−i−iii−3−333000011-1-133−3−3i3i3−i3−i300000000000000000000
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χ43222-2-2-1-222-2-111−2i−2i2i2i-112i2i−2i−2i-22-221-11-1ii−i−i1-1−i−iii1-100−2i2i00−i3−i3i3i32-2ii−i−i−3−3330000-1-111−3−333−i3−i3i3i300000000000000000000
χ44222-2-2-1-222-2-111−2i−2i2i2i-112i2i−2i−2i-22-221-11-1ii−i−i1-1−i−iii1-100−2i2i00i3i3−i3−i32-2ii−i−i33−3−30000-1-11133−3−3i3i3−i3−i300000000000000000000
χ4522-22-222-22-22222i−2i2i−2i-2-22i−2i2i−2i2-2-2222-2-22i−2i2i−2i-222i−2i2i−2i2-2000000000000000000002-22i−2i00002-22-22i−2i2i−2i00000000000000000000
χ4622-22-222-22-22222i−2i2i−2i-2-22i−2i2i−2i2-2-2222-2-22i−2i2i−2i-222i−2i2i−2i2-200000000000000000000-22−2i2i0000-22-22−2i2i−2i2i00000000000000000000
χ4722-22-222-22-22222i−2i2i−2i-2-2−2i2i−2i2i-222-222-2-22i−2i2i−2i2-2−2i2i−2i2i-2200000000000000000000000000000000000000000000000000002i−2i2-2
χ4822-22-222-22-22222i−2i2i−2i-2-2−2i2i−2i2i-222-222-2-22i−2i2i−2i2-2−2i2i−2i2i-220000000000000000000000000000000000000000000000000000−2i2i-22
χ4922-22-222-22-2222−2i2i−2i2i-2-22i−2i2i−2i-222-222-2-2−2i2i−2i2i2-22i−2i2i−2i-2200000000000000000000000000000000000000000000000000002i−2i-22
χ5022-22-222-22-2222−2i2i−2i2i-2-22i−2i2i−2i-222-222-2-2−2i2i−2i2i2-22i−2i2i−2i-220000000000000000000000000000000000000000000000000000−2i2i2-2
χ5122-22-222-22-2222−2i2i−2i2i-2-2−2i2i−2i2i2-2-2222-2-2−2i2i−2i2i-22−2i2i−2i2i2-2000000000000000000002-2−2i2i00002-22-2−2i2i−2i2i00000000000000000000
χ5222-22-222-22-2222−2i2i−2i2i-2-2−2i2i−2i2i2-2-2222-2-2−2i2i−2i2i-22−2i2i−2i2i2-200000000000000000000-222i−2i0000-22-222i−2i2i−2i00000000000000000000
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χ5622-22-2-12-22-2-1-1-12i−2i2i−2i112i−2i2i−2i2-2-22-1-111−ii−ii1-1−ii−ii-11000000i3−i3i3−i300i3−i3i3−i3−33−332-22i−2i−33−33-11-11−ii−ii00000000000000000000
χ5722-22-2-12-22-2-1-1-1−2i2i−2i2i11−2i2i−2i2i2-2-22-1-111i−ii−i1-1i−ii−i-11000000−i3i3−i3i300−i3i3−i3i3−33−332-2−2i2i−33−33-11-11i−ii−i00000000000000000000
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χ6022-22-2-12-22-2-1-1-1−2i2i−2i2i11−2i2i−2i2i2-2-22-1-111i−ii−i1-1i−ii−i-11000000i3−i3i3−i300i3−i3i3−i33−33−32-2−2i2i3−33−3-11-11i−ii−i00000000000000000000
χ6122-2-222-2-2222-2-22-2-22-222-2-2222-2-2-222-22-2-22-2-22-2-22220000000000000000000000000000000000000000000020-202-2000000
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χ7522-2-22-1-2-222-111-222-21-12-2-22-2-2221-1-111-1-11-1-1-111-111-22002-21-1-11003−3−33-111-100003−3−33−333−3−333−300000000000000000000
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χ8844-44-4-24-44-4-2-2-2−4i4i−4i4i224i−4i4i−4i-444-4-2-2222i−2i2i−2i-22−2i2i−2i2i2-200000000000000000000000000000000000000000000000000000000
χ8944-4-44444-4-44-4-40000-44000000004-4-440000000000000000000000000000000000000000000000004-4000000000000000000
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Here i is the imaginary unit (i² = −1).