Finite Group Databasebeta

← Group #373613

Character table — Group #373613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444444444444444444444448888888888888888444444444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111
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χ1811-1-1-111111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1ii−i−i11-1-1−i−i−i−iiiii-1-1-1-111111-1i−i11-1-1−i−iii-1-111ii−i−iii−i−i-1-111−i−iii-11−ii
χ1911-1-1-111111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1−i−iii-1-111iiii−i−i−i−i1111-1-1-1-1-11−ii-1-111ii−i−i11-1-1ii−i−i−i−iii-1-111−i−iii-11−ii
χ2011-1-1-111111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1−i−iii-1-111−i−i−i−iiiii-1-1-1-11111-11−ii-1-111−i−iii-1-111ii−i−i−i−iii11-1-1ii−i−i1-1i−i
χ2111-1-1-111111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1i−i-1-111−i−iii-1-111−i−iii−i−iii11-1-1ii−i−i-11−ii
χ2211-1-1-111111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111ii−i−i11-1-1−i−i−i−iiiii-1-1-1-111111-1i−i-1-111ii−i−i11-1-1−i−iii−i−iii-1-111−i−iii1-1i−i
χ2311-1-1-111111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−iii-1-111iiii−i−i−i−i1111-1-1-1-1-11−ii11-1-1−i−iii-1-111−i−iiiii−i−i-1-111−i−iii1-1i−i
χ2411-1-1-111111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−iii-1-111−i−i−i−iiiii-1-1-1-11111-11−ii11-1-1ii−i−i11-1-1−i−iiiii−i−i11-1-1ii−i−i-11−ii
χ2511-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i-1-1-1-11111-11i−i-1-111ii−i−i-1-111−i−iiiii−i−i11-1-1−i−iii1-1−ii
χ2611-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1ii−i−i-1-111−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111−i−iii11-1-1−i−iiiii−i−i-1-111ii−i−i-11i−i
χ2711-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−iii11-1-1iiii−i−i−i−i-1-1-1-111111-1−ii11-1-1ii−i−i-1-111−i−iii−i−iii-1-111ii−i−i-11i−i
χ2811-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii1-1−ii
χ2911-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111ii−i−i-1-111iiii−i−i−i−i-1-1-1-11111-11i−i11-1-1−i−iii11-1-1ii−i−i−i−iii11-1-1−i−iii-11i−i
χ3011-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111ii−i−i-1-111−i−i−i−iiiii1111-1-1-1-1-11i−i11-1-1ii−i−i-1-111ii−i−i−i−iii-1-111ii−i−i1-1−ii
χ3111-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111−i−iii11-1-1iiii−i−i−i−i-1-1-1-111111-1−ii-1-111−i−iii11-1-1ii−i−iii−i−i-1-111ii−i−i1-1−ii
χ3211-1-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii-1-111ii−i−i-1-111ii−i−iii−i−i11-1-1−i−iii-11i−i
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χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-2000000000000000022-2-200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-222220000000000000000-2-22200000000000000000000000000000000
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χ382222-22-22-2-22-2-2-2-22-2-22-200000000222-200002i2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000-22-22000000000000000000000000
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χ832-2-22222-2-2-2-2-22-222-222-2−2i2i−2i2i2i−2i2i−2i2-2-222i−2i−2i2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002-2-220000000000000000
χ842-2-22222-2-2-2-2-22-222-222-2−2i2i−2i2i2i−2i2i−2i2-2-222i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000-222-20000000000000000
χ852-2-22-22-2-222-22-22-222-222000000002-2-2-200002-22-2-22-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000002i−2i−2i2i00000000000000000000
χ862-2-22-22-2-222-22-22-222-222000000002-2-2-200002-22-2-22-220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000−2i2i2i−2i00000000000000000000
χ872-2-22-22-2-222-22-22-222-222000000002-2-2-20000-22-222-22-200000000000000002i−2i2i−2i−2i2i−2i2i000000000000−2i2i2i−2i00000000000000000000
χ882-2-22-22-2-222-22-22-222-222000000002-2-2-20000-22-222-22-20000000000000000−2i2i−2i2i2i−2i2i−2i0000000000002i−2i−2i2i00000000000000000000
χ894444-44-44-4-44-4-4-4-4444-4400000000-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4-44-4-44-4-444-440000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ91444-4-4-44-4-44-4-444-44000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ9244-444-44-4-4444-4-4-4-400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ9344-444-44-4-4444-4-4-4-4000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ9444-4-444-44-4-4-4444-4-4444-400000000-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ954-4444-4444-4-4-4-44-4-40000000000000000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ964-4444-4444-4-4-4-44-4-400000000000000000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ974-444-4-4-44-44-444-44-400004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-44-44-444-44-40000−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ994-44-444-4-4444-44-4-4-4-444400000000-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-4-44-44-4-444-44-44-44-44-4-400000000-4444000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-44-4-44-444-4-444400004-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-44-4-44-444-4-44440000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4444-4444-4-440000000000000000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ1044-4-4-4-4-4444-4444-4-4400000000000000000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000

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