Finite Group Databasebeta

← Group #72322785

Character table — Group #72322785

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size112222222222222444444444444444448888888888888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161664646464646464646464646464646464
order12222444488161616164444888888816161616161616161616323232323232323232323232323232328888161616163232323232323232646464646464646464646464646464646464646464646464646464646464646422444488888816161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
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χ1811-1-11-111-111-1-1-1-111-1-1-1-11-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111i−ii−ii−ii−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-11−ii-11−ii−ii−ii-11-11
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χ2411-1-11-111-111-1-1-1-111-1-1-1-11-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111−ii−ii−ii−ii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-11i−i-11i−ii−ii−i-11-11
χ2511-1-11-111-111-1-1-1-1-1-111-1-1111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11-1-111-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1i−i-11−ii1-1-11−iii−i
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χ3011-1-11-111-111-1-1-1-1-1-111-1-1111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11−ii1-1i−i1-1-11−iii−i
χ3111-1-11-111-111-1-1-1-1-1-111-1-1111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1−ii-11i−i-111-1−iii−i
χ3211-1-11-111-111-1-1-1-1-1-111-1-1111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11i−i1-1−ii1-1-11i−i−ii
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χ36222222222222222-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-22222−2i−2i2i2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
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χ4022222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2222200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
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χ54222-2-2-22-2222-2-2-2-22i−2i2i−2i2-2-22i−2i2i−2i22-2-222−2i2i−2i2i22-2-22i2i−2i−2i22-2-22i2i−2i−2i00000000000000000000000000000000−2ζ22ζ22ζ2−2ζ2−2ζ22ζ22ζ2−2ζ22ζ6−2ζ6−2ζ62ζ62ζ6−2ζ6−2ζ62ζ60000000000000000
χ55222-2-2-22-2222-2-2-2-22i−2i2i−2i2-2-22i−2i2i−2i22-2-222−2i2i−2i2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i00000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-2200000000000000000000000000000000
χ56222-2-2-22-2222-2-2-2-22i−2i2i−2i2-2-22i−2i2i−2i22-2-222−2i2i−2i2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i0000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-200000000000000000000000000000000
χ57222-2-2-22-2222-2-2-2-2−2i2i−2i2i2-2-2−2i2i−2i2i22-2-2222i−2i2i−2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000000000002ζ6−2ζ6−2ζ62ζ62ζ6−2ζ6−2ζ62ζ6−2ζ22ζ22ζ2−2ζ2−2ζ22ζ22ζ2−2ζ20000000000000000
χ58222-2-2-22-2222-2-2-2-2−2i2i−2i2i2-2-2−2i2i−2i2i22-2-2222i−2i2i−2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00000000000000000000000000000000−2ζ62ζ62ζ6−2ζ6−2ζ62ζ62ζ6−2ζ62ζ2−2ζ2−2ζ22ζ22ζ2−2ζ2−2ζ22ζ20000000000000000
χ59222-2-2-22-2222-2-2-2-2−2i2i−2i2i2-2-2−2i2i−2i2i22-2-2222i−2i2i−2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i00000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-200000000000000000000000000000000
χ60222-2-2-22-2222-2-2-2-2−2i2i−2i2i2-2-2−2i2i−2i2i22-2-2222i−2i2i−2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i0000000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-2200000000000000000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.