Finite Group Databasebeta

← Group #72270552

Character table — Group #72270552

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size112222222222244444444444444444488888888888888888888121212121212121216161616161616161616161616161616161616161616161616161616161616162424242424242424242424244848484848484848
order1222234444612124444666888888881212121212121216161616161616162424242424242424224488882444446688121212121212121212122424242448484848484848484488161616161616161622444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ91111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ101111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ121111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ131111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ141111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
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χ161111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
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χ2011-1-111-111-11-1-111-1-1-1-111111-1-1-1-1-11111-1-1ii−i−iii−i−i1111-1-1-1-1-11-11-1-111-11−ii-11-1-1−ii11−i−iii-1-111−i−iiiii−i−iii−i−i-11-11−i−iii−i−iii1-1i−i1-1i−i
χ2111-1-111-111-11-1-111-1-1-1-111111-1-1-1-1-11111-1-1−i−iii−i−iii1111-1-1-1-11-11-111-1-11-1−ii1-111−ii-1-1−i−iii11-1-1−i−iii−i−iii−i−iii1-11-1−i−iii−i−iii1-1−ii1-1−ii
χ2211-1-111-111-11-1-111-1-1-1-111111-1-1-1-1-11111-1-1−i−iii−i−iii1111-1-1-1-11-11-111-1-1-11i−i-11-1-1i−i11ii−i−i-1-111ii−i−i−i−iii−i−iii1-11-1−i−iii−i−iii-11i−i-11i−i
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χ2511-1-111-111-11-1-1-1-111-1-1111-1-111-1-1-111-1-111ii−i−i−i−iii11-1-111-1-11-11-111-1-11-1i−i-1111−ii-1-1ii−i−i-1-111−i−iiiii−i−i−i−iii-11-11ii−i−i−i−iii-11i−i1-1−ii
χ2611-1-111-111-11-1-1-1-111-1-1111-1-111-1-1-111-1-111ii−i−i−i−iii11-1-111-1-11-11-111-1-1-11−ii1-1-1-1i−i11−i−iii11-1-1ii−i−iii−i−i−i−iii-11-11ii−i−i−i−iii1-1−ii-11i−i
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χ7922-2-222-222-22-2-2-2-222-2-22-2-222-2-222-222-2-22200000000-2-222-2-2222-22-2-2-22200000000000000000000000000000000-222-20000000000000000
χ8022-2-222-222-22-2-2-2-222-2-22-2-222-2-222-222-2-22200000000-2-222-2-222-22-2222-2-2000000000000000000000000000000002-2-220000000000000000
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χ8722-2-22-1-222-2-111-2-22211-122-2-222-2-21-1-111-1-1−2i−2i2i2i2i2i−2i−2i-1-111-1-111000000002-2−2i2i-22-1-12i−2i11ii−i−i11-1-1−i−iiiii−i−i−i−iii00000000000000000000
χ8822-2-22-1-222-2-111-2-22211-122-2-222-2-21-1-111-1-1−2i−2i2i2i2i2i−2i−2i-1-111-1-11100000000-222i−2i2-211−2i2i-1-1−i−iii-1-111ii−i−iii−i−i−i−iii00000000000000000000
χ89444444-4-4-4-44-4-4000044400000000-4-4-4000000000000000000004-4-4400000000000000000000000000000000000000000000000000000000
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χ9144444-24444-2-2-24444-2-2-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-20000000022222222000000000000000000000000000000000000000000000000000000000000
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χ93444-4-444-44-44440000-44-400000000-4-440000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ94444-4-444-44-44440000-44-400000000-4-44000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ95444-4-4-2-44-44-2224i−4i4i−4i2-224-44i−4i4i−4i4-4-2-22−2i2i−2i2i00000000-22−2i2i−2i2i-22000000000000000000000000000000000000000000000000000000000000
χ96444-4-4-2-44-44-222−4i4i−4i4i2-224-4−4i4i−4i4i4-4-2-222i−2i2i−2i00000000-222i−2i2i−2i-22000000000000000000000000000000000000000000000000000000000000
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χ10044-44-4-244-4-4-2-2-2−4i4i4i−4i-2224-4−4i4i4i−4i-442-222i−2i−2i2i00000000-222i−2i−2i2i2-2000000000000000000000000000000000000000000000000000000000000
χ10144-4-4444-4-444440000-4-44000000004-4-40000000000000000000044-4-400000000000000000000000000000000000000000000000000000000
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χ10344-4-44-2-444-4-22244-4-422-2-4-4-4-444442-2-2-2-222000000002222-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ10444-4-44-2-444-4-222-4-44422-2-4-444-4-4442-2-222-2-20000000022-2-222-2-2000000000000000000000000000000000000000000000000000000000000
χ10588888-4-8-8-8-8-4440000-4-4-40000000044400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ106888-8-8-48-88-8-4-4-400004-440000000044-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10788-88-8-4-8-888-4440000-44400000000-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10888-8-88-48-8-88-4-4-4000044-400000000-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10916-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000-80000883−8300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11116-16000-800008−838300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).