Finite Group Databasebeta

← Group #108459

Character table — Group #108459

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444444444444444444488888888888888888888888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ181111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii
χ191111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ201111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i
χ211111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ221111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i
χ231111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ241111-1-1-1111-1-1-1-11-1111111-1-1-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii
χ251111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-1
χ261111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-111
χ271111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111
χ281111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1
χ291111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-11111-1-1−i−iiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii11-1-1-1-111
χ301111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-11111-1-1−i−iiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-1
χ311111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-11111-1-1−i−iiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1
χ321111-1-1-1111-1-1-1-11-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-11111-1-1−i−iiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111
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χ342222222222222222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-22-22-2-2-2-2-22222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2222-2-2-222222222222-22-22-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2222-2-2-2222-2-2-2-2-2-2-2-2-22-22-2-2-2-2222222-2-222-2-2000000000000000000000000000000000000000000000000
χ372222-2-2-2222-2-2-2-22-2222-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i2-2-22-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ382222-2-2-2222-2-2-2-22-2222-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i2-2-22-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ392222-2-2-2222-2-2-2-22-2-2-2-2222222-2-2-22i2i2i2i−2i−2i−2i−2i-222-2-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ402222-2-2-2222-2-2-2-22-2-2-2-2222222-2-2-2−2i−2i−2i−2i2i2i2i2i-222-2-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4122-2-222-22-2-222-2-22-200022-20002-2-22i2i−2i−2i2i2i−2i−2i0-20200000000002i−2i002i−2i0000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ4222-2-222-22-2-222-2-22-200022-20002-2-22i2i−2i−2i2i2i−2i−2i0-20200000000002i−2i002i−2i0000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ4322-2-222-22-2-222-2-22-200022-20002-2-2−2i−2i2i2i−2i−2i2i2i0-2020000000000−2i2i00−2i2i0000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ4422-2-222-22-2-222-2-22-200022-20002-2-2−2i−2i2i2i−2i−2i2i2i0-2020000000000−2i2i00−2i2i0000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ4522-2-222-22-2-222-2-22-2000-2-22000-2222i2i−2i−2i2i2i−2i−2i020-20000000000−2i2i00−2i2i00000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ4622-2-222-22-2-222-2-22-2000-2-22000-2222i2i−2i−2i2i2i−2i−2i020-20000000000−2i2i00−2i2i0000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4722-2-222-22-2-222-2-22-2000-2-22000-222−2i−2i2i2i−2i−2i2i2i020-200000000002i−2i002i−2i00000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ4822-2-222-22-2-222-2-22-2000-2-22000-222−2i−2i2i2i−2i−2i2i2i020-200000000002i−2i002i−2i0000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4922-2-2-2-222-2-2-2-2222200022-2000-22222-2-2-2-2220-20-200000000002-200-220000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5022-2-2-2-222-2-2-2-2222200022-2000-22222-2-2-2-2220-20-200000000002-200-220000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5122-2-2-2-222-2-2-2-2222200022-2000-222-2-22222-2-20-20-20000000000-22002-20000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5222-2-2-2-222-2-2-2-2222200022-2000-222-2-22222-2-20-20-20000000000-22002-20000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5322-2-2-2-222-2-2-2-22222000-2-220002-2-222-2-2-2-22202020000000000-22002-200000000000000002−2−22−222−2−222−22−2−220000000000000000
χ5422-2-2-2-222-2-2-2-22222000-2-220002-2-222-2-2-2-22202020000000000-22002-20000000000000000−222−22−2−222−2−22−222−20000000000000000
χ5522-2-2-2-222-2-2-2-22222000-2-220002-2-2-2-22222-2-2020200000000002-200-2200000000000000002−2−22−222−22−2−22−222−20000000000000000
χ5622-2-2-2-222-2-2-2-22222000-2-220002-2-2-2-22222-2-2020200000000002-200-220000000000000000−222−22−2−22−222−22−2−220000000000000000
χ572-22-22-22-22-22-22-22-222-20002-2-20002i−2i2i−2i2i−2i2i−2i-2020000000002i−2i002i−2i0000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2
χ582-22-22-22-22-22-22-22-222-20002-2-20002i−2i2i−2i2i−2i2i−2i-2020000000002i−2i002i−2i0000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22
χ592-22-22-22-22-22-22-22-222-20002-2-2000−2i2i−2i2i−2i2i−2i2i-202000000000−2i2i00−2i2i0000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22
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χ612-22-22-22-22-22-22-22-2-2-22000-2220002i−2i2i−2i2i−2i2i−2i20-2000000000−2i2i00−2i2i00000000000000000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2
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χ632-22-22-22-22-22-22-22-2-2-22000-222000−2i2i−2i2i−2i2i−2i2i20-20000000002i−2i002i−2i00000000000000000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2
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χ652-22-2-22-2-22-2-22-222222-2000-2220002-22-2-22-22-20-20000000002-200-220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2
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χ672-22-2-22-2-22-2-22-222222-2000-222000-22-222-22-2-20-2000000000-22002-20000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2
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χ692-22-2-22-2-22-2-22-2222-2-220002-2-20002-22-2-22-22202000000000-22002-200000000000000000000000000000000002−2−22−222−2−222−22−2−22
χ702-22-2-22-2-22-2-22-2222-2-220002-2-20002-22-2-22-22202000000000-22002-20000000000000000000000000000000000−222−22−2−222−2−22−222−2
χ712-22-2-22-2-22-2-22-2222-2-220002-2-2000-22-222-22-22020000000002-200-2200000000000000000000000000000000002−2−22−222−22−2−22−222−2
χ722-22-2-22-2-22-2-22-2222-2-220002-2-2000-22-222-22-22020000000002-200-220000000000000000000000000000000000−222−22−2−22−222−22−2−22
χ732-2-2-2222222-2-2-2-2-222-222-2222-222-200000000-2-2-2-22-22-2000000000000000000002-22-22-22-200000000000000000000000000000000
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χ882-2-2-2-2-2-22222222-2-2-22-2-22-222-222-20000000022-2-22-2-2200000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ89444-44-4-4-4-44-444-4-4400000000000000000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ90444-44-4-4-4-44-444-4-440000000000000000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ91444-4-444-4-444-4-44-4-400000000000000000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ92444-4-444-4-444-4-44-4-40000000000000000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ9344-444-44-44-4-44-44-4-44-4-40004-440000000000040-400000000000000000000000000000000000000000000000000000000000000000
χ9444-444-44-44-4-44-44-4-4-444000-44-400000000000-40400000000000000000000000000000000000000000000000000000000000000000
χ9544-44-44-4-44-44-44-4-444-4-4000-44-40000000000040400000000000000000000000000000000000000000000000000000000000000000
χ9644-44-44-4-44-44-44-4-44-4440004-4400000000000-40-400000000000000000000000000000000000000000000000000000000000000000
χ974-44444-44-4-4-4-444-4-40004-4-40004-4400000000040-40000000000000000000000000000000000000000000000000000000000000000
χ984-44444-44-4-4-4-444-4-4000-444000-44-4000000000-4040000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-444-4-444-4-4-440004-4-4000-44-40000000004040000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-444-4-444-4-4-44000-4440004-44000000000-40-40000000000000000000000000000000000000000000000000000000000000000
χ1014-4-444-4-4-4-444-4-44440000000000004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-444-4-4-4-444-4-4444000000000000-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-4-44-444-44-40000000000004i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-4-44-444-44-4000000000000−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

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