Finite Group Databasebeta

← Group #147159

Character table — Group #147159

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order122244448888888822222244444488888888888816161616161616161616161616161616444444444444888888888888161616161616161616161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111
χ9111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ10111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111
χ13111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111
χ14111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−iii11-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111
χ15111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1
χ16111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111−i−iiiii−i−i-1-111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1
χ1711111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ1811111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ1911111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ2011111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ2111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ2211111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ2311111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ2411111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-1111111111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ2511111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−iii−i−i-1-111−i−iii−i−iii-1-11111-1-1-1-11111-1-1ii−i−i−i−iii
χ2611111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iii−i−iii-1-111ii−i−iii−i−i11-1-1-1-11111-1-1-1-111ii−i−i−i−iii
χ2711111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i-1-11111-1-111-1-1-1-111−i−iiiii−i−i
χ2811111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii11-1-1-1-111-1-11111-1-1−i−iiiii−i−i
χ2911111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−iii−i−i-1-111−i−iii−i−iii11-1-1-1-11111-1-1-1-111−i−iiiii−i−i
χ3011111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii−i−iii-1-111ii−i−iii−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i
χ3111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i11-1-1-1-111-1-11111-1-1ii−i−i−i−iii
χ3211111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii-1-11111-1-111-1-1-1-111ii−i−i−i−iii
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χ362222222222222222-2-2-22-22-2-2-22-22-2-2-2-222-2-222-2-200000000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ3722222222-2-2-2-2-2-2-2-2-2-22-22-2-2-22-22-222-2-222-2-22222000000000000000000000000000000000000000000000000000000002-2-222-2-22
χ3822222222-2-2-2-2-2-2-2-2-2-22-22-2-2-22-22-222-2-222-2-2222200000000000000000000000000000000000000000000000000000000-222-2-222-2
χ3922222222-2-2-2-2-2-2-2-2-2-2-22-22-2-2-22-222222-2-222-2-222000000000000000000000000000000000000000000000000000000002-2-22-222-2
χ4022222222-2-2-2-2-2-2-2-2-2-2-22-22-2-2-22-222222-2-222-2-22200000000000000000000000000000000000000000000000000000000-222-22-2-22
χ412222-2-2-2-22i2i2i2i−2i−2i−2i−2i222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000002-22-2000000002i−2i2i−2i00000000000000000000000000000000
χ422222-2-2-2-22i2i2i2i−2i−2i−2i−2i222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000-22-2200000000−2i2i−2i2i00000000000000000000000000000000
χ432222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-2-2-2-2-222222i−2i−2i2i−2i2i−2i2i−2i2i2i−2i00000000000000002-2-22000000002i−2i−2i2i00000000000000000000000000000000
χ442222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-2-2-2-2-222222i−2i−2i2i−2i2i−2i2i−2i2i2i−2i0000000000000000-222-200000000−2i2i2i−2i00000000000000000000000000000000
χ452222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-22-22-222-22-22−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i2ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ2000000000000000000000000000000000000000000000000
χ462222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-22-22-222-22-22−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ2000000000000000000000000000000000000000000000000
χ472222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-22-22222-22-2−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ2−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ2000000000000000000000000000000000000000000000000
χ482222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-22-22222-22-2−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ22ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ2000000000000000000000000000000000000000000000000
χ492222-2-2-2-2−2i−2i−2i−2i2i2i2i2i222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000002-22-200000000−2i2i−2i2i00000000000000000000000000000000
χ502222-2-2-2-2−2i−2i−2i−2i2i2i2i2i222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000-22-22000000002i−2i2i−2i00000000000000000000000000000000
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χ542222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-22-22-222-22-222i−2i−2i2i2i−2i−2i2i2i−2i2i−2i−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6000000000000000000000000000000000000000000000000
χ552222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-22-22222-22-22i−2i2i−2i−2i2i2i−2i−2i2i2i−2i2ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6000000000000000000000000000000000000000000000000
χ562222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-22-22222-22-22i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ62ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6000000000000000000000000000000000000000000000000
χ5722-2-222-2-222-2-222-2-22-222-2-22-222-2-22222-2-2-2-222-2-20000000000000000000000000000000000000000000000002-22-22-22-200000000
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χ6222-2-222-2-222-2-222-2-2-222-2-22-222-2-22-2-22222-2-2-2-22200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000000000000000000000
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χ6422-2-222-2-222-2-222-2-2-22-222-2-22-222-2-2-2-2-2-2-222222200000000000000000000-222-200000000-222-20000000000000000000000000000
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χ6622-2-222-2-2-2-222-2-2222-222-2-22-222-2-2-2-2-2-22222-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
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χ7022-2-222-2-2-2-222-2-222-222-2-22-222-2-2222-2-2-2-22222-2-200000000000000000000−2i2i−2i2i000000002i−2i2i−2i0000000000000000000000000000
χ7122-2-222-2-2-2-222-2-222-22-222-2-22-222-2222222-2-2-2-2-2-2000000000000000000002-2-2200000000-222-20000000000000000000000000000
χ7222-2-222-2-2-2-222-2-222-22-222-2-22-222-2222222-2-2-2-2-2-200000000000000000000-222-2000000002-2-220000000000000000000000000000
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χ7622-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-2-2-222-2222-2-22i−2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000−2ζ62ζ62ζ2−2ζ22ζ6−2ζ6−2ζ22ζ20000000000000000
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χ1034-4-44−4i4i4i−4i−4ζ64ζ64ζ6−4ζ6−4ζ24ζ24ζ2−4ζ20000000000000000000000002ζ3+2ζ7−2ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ+2ζ52ζ−2ζ52ζ+2ζ5−2ζ−2ζ500000000000000000000000000000000000000000000000000000000
χ1044-4-44−4i4i4i−4i−4ζ64ζ64ζ6−4ζ6−4ζ24ζ24ζ2−4ζ2000000000000000000000000−2ζ3−2ζ72ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ−2ζ5−2ζ+2ζ5−2ζ−2ζ52ζ+2ζ500000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.