Finite Group Databasebeta

← Group #147155

Character table — Group #147155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order1222222244444444222244448888888888888888444444448888888844444444888888881616161616161616161616161616161616161616161616161616161616161616
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ10111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1
χ181111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-1-111-1-111-1-111-1-111
χ191111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-1-111-1-111-1-111-1-111
χ201111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1
χ211111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-1-111-1-111
χ221111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-111-1-1
χ231111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-111-1-1
χ241111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-1-111-1-111
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii11-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i11-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
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χ3522222222-2-2-2-2-2-2-2-22222-2-2-2-2−2i−2i−2i2i2i2i−2i−2i2i2i−2i−2i2i2i−2i2i22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-22222-2-2-2-2−2i−2i−2i2i2i2i−2i−2i2i2i−2i−2i2i2i−2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-2-2-222222i2i2i−2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i−2i22-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-2-2-222222i2i2i−2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i−2i-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
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χ53222-2-22-2-2-2-222-2-222-2-22222-2-22i2i−2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ54222-2-22-2-2-2-222-2-222-2-22222-2-22i2i−2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ55222-2-22-2-2-2-222-2-222-2-22222-2-2−2i−2i2i2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ56222-2-22-2-2-2-222-2-222-2-22222-2-2−2i−2i2i2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
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χ702-2-2222-2-2-2-22222-2-2-22-222-22-22-22-222-2-2-2-22222-2-20000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000000000000000
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χ722-2-2222-2-2-2-22222-2-2-22-222-22-2-22-22-2-22222-2-2-2-2220000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000000000000000
χ732-2-2-2-22222222-2-2-2-22-2-222-2-222i−2i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000
χ742-2-2-2-22222222-2-2-2-22-2-222-2-222i−2i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000
χ752-2-2-2-22222222-2-2-2-22-2-222-2-22−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000
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χ772-2-2-2-22222222-2-2-2-2-222-2-222-22i−2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000
χ782-2-2-2-22222222-2-2-2-2-222-2-222-22i−2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000
χ792-2-2-2-22222222-2-2-2-2-222-2-222-2−2i2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000
χ802-2-2-2-22222222-2-2-2-2-222-2-222-2−2i2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000
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χ872-2-2-2-2222-2-2-2-22222-222-22-2-22-2222-222-22-2-22-22-2-2000000000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i
χ882-2-2-2-2222-2-2-2-22222-222-22-2-22-2222-222-22-2-22-22-2-200000000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i
χ8944-44-4-44-44i−4i4i−4i4i−4i4i−4i0000000000000000000000000000000000004ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000000000
χ9044-44-4-44-44i−4i4i−4i4i−4i4i−4i000000000000000000000000000000000000−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000000000
χ9144-44-4-44-4−4i4i−4i4i−4i4i−4i4i0000000000000000000000000000000000004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000
χ9244-44-4-44-4−4i4i−4i4i−4i4i−4i4i000000000000000000000000000000000000−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000000000
χ9344-4-44-4-444i−4i−4i4i4i−4i−4i4i0000000000000000000000004i−4i4-4000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000−4i4i-44000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-44−4i4i4i−4i−4i4i4i−4i0000000000000000000000004i−4i-44000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000−4i4i4-4000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000000000
χ984-444-4-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000000000
χ994-444-4-4-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000000000
χ1004-444-4-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000000000
χ1014-44-44-44-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000004-44i−4i00000000000000000000000000000000000000000000000000000000
χ1024-44-44-44-44i−4i4i−4i−4i4i−4i4i0000000000000000000000000000-44−4i4i00000000000000000000000000000000000000000000000000000000
χ1034-44-44-44-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000004-4−4i4i00000000000000000000000000000000000000000000000000000000
χ1044-44-44-44-4−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000-444i−4i00000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.