Finite Group Databasebeta

← Group #359367

Character table — Group #359367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1711-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1811-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-1-111−i−iii
χ1911-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ2011-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i
χ2111-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ2211-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i
χ2311-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ2411-111-1-1-1111-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii
χ2511-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ2611-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i
χ2711-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ2811-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii
χ2911-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ3011-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii
χ3111-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ3211-111-1-1-1111-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i
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χ342222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ372222-222-22-2-22-2-2-2-2222222-2-222-2-222-2-222-2-2-2-2-2-2000000000000000000000000000000002-22-22-22-2000000000000000000000000
χ382222-222-22-2-22-2-2-2-2222222-2-222-2-222-2-222-2-2-2-2-2-200000000000000000000000000000000-22-22-22-22000000000000000000000000
χ392222-222-22-2-22-2-2-2-22222-2-222-2-222-2-222-2-222-2-2-2-2000000000000000000000000000000002-22-2-22-22000000000000000000000000
χ402222-222-22-2-22-2-2-2-22222-2-222-2-222-2-222-2-222-2-2-2-200000000000000000000000000000000-22-222-22-2000000000000000000000000
χ412222-222-22-2-22-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222222200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ422222-222-22-2-22-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222220000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ432222-222-22-2-22-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2222200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ442222-222-22-2-22-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222220000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
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χ4622-222-2-2-2222-2-2-22-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-222-2-222−2i−2i2i2i22-2-22i2i−2i−2i000000000000000000000000000000000000000000000000
χ4722-222-2-2-2222-2-2-22-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-22222-2-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ4822-222-2-2-2222-2-2-22-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-222-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4922-22-2-2-222-2-2-222-2222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ5022-22-2-2-222-2-2-222-2222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2-22200000000000000000000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ5122-22-2-2-222-2-2-222-2222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2-222000000000000000000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ5222-22-2-2-222-2-2-222-2222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2-22200000000000000000000000000000000-222-22i−2i−2i2i000000000000000000000000
χ5322-22-2-2-222-2-2-222-22-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i22-2-200000000000000000000000000000000000000002i−2i−2i2i-222-20000000000000000
χ5422-22-2-2-222-2-2-222-22-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i22-2-20000000000000000000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ5522-22-2-2-222-2-2-222-22-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i22-2-200000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ5622-22-2-2-222-2-2-222-22-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i22-2-20000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000000000
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χ582-2222-2-2-2-2-2-22222-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000−2i2i−2i2i-22-2200000000000000000000000000000000
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χ622-2222-2-2-2-2-2-22222-2-22-222i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i-22-220000000000000000−2i2i−2i2i-22-220000000000000000000000000000000000000000
χ632-2222-2-2-2-2-2-22222-2-22-22−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i-22-2200000000000000002i−2i2i−2i-22-220000000000000000000000000000000000000000
χ642-2222-2-2-2-2-2-22222-2-22-22−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i-22-220000000000000000−2i2i−2i2i2-22-20000000000000000000000000000000000000000
χ652-222-2-2-22-2222-2-2-222-22-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i-22-22000000000000000000000000000000000000000000000000000000002i−2i2i−2i2-22-2
χ662-222-2-2-22-2222-2-2-222-22-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i-22-2200000000000000000000000000000000000000000000000000000000−2i2i−2i2i-22-22
χ672-222-2-2-22-2222-2-2-222-22-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i-22-22000000000000000000000000000000000000000000000000000000002i−2i2i−2i-22-22
χ682-222-2-2-22-2222-2-2-222-22-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i-22-2200000000000000000000000000000000000000000000000000000000−2i2i−2i2i2-22-2
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χ702-222-2-2-22-2222-2-2-22-22-222i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i-22-2200000000
χ712-222-2-2-22-2222-2-2-22-22-22−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i2-22-20000000000000000000000000000000000000000000000002i−2i2i−2i-22-2200000000
χ722-222-2-2-22-2222-2-2-22-22-22−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i2-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i2-22-200000000
χ732-2-222222-2-2-2-2-2-2222-2-222-22-22-22-2-22-22-22-222-2-220000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ742-2-222222-2-2-2-2-2-2222-2-222-22-22-22-2-22-22-22-222-2-22000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ752-2-222222-2-2-2-2-2-2222-2-22-22-22-22-222-22-22-22-22-2-220000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ762-2-222222-2-2-2-2-2-2222-2-22-22-22-22-222-22-22-22-22-2-22000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ772-2-222222-2-2-2-2-2-222-222-22-22-2-22-22-22-222-22-2-222-200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000
χ782-2-222222-2-2-2-2-2-222-222-22-22-2-22-22-22-222-22-2-222-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000
χ792-2-222222-2-2-2-2-2-222-222-2-22-222-22-22-22-2-22-22-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ802-2-222222-2-2-2-2-2-222-222-2-22-222-22-22-22-2-22-22-222-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
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χ89444-444-44-44-4-44-4-4-400000000000000000000000000004-44-400000000000000000000000000000000000000000000000000000000
χ90444-444-44-44-4-44-4-4-40000000000000000000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ91444-4-44-4-4-4-44-4-44440000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ92444-4-44-4-4-4-44-4-4444000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-44-4-44-44-44-4400000000000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ9444-4-44-44-4-44-44-44-440000000000000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ9544-4-4-4-444-4-4444-44-40000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-4-444-4-4444-44-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ974-44-44-44-44-44-44-4-44000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ984-44-44-44-44-44-44-4-4400000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ994-44-4-4-44444-4-4-444-40000000000000000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ1004-44-4-4-44444-4-4-444-4000000000000000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ1014-4-4-444-444-444-44-4-4000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ1024-4-4-444-444-444-44-4-400000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ1034-4-4-4-44-4-444-444-4440000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ1044-4-4-4-44-4-444-444-444000000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000

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