Finite Group Databasebeta

← Group #109521

Character table — Group #109521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222444444442222444444444444444444448888888888888888444444448888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−iiiiiii−i−i−i−i−i−iii-1-1-1-11111−i−i−i−iiiii-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1ii−i−i−i−i−i−iiiiiii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−iiiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111
χ171-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−iii−i−iii−i−ii−ii−iii−i−iii−i−i11-1-111-1-111-1-111-1-1
χ181-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−ii−iiii−i−iii−i−i−ii−ii−i−iii−i−iii-1-111-1-111-1-111-1-111
χ191-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1−i−iii−i−iiii−ii−i−i−iii−i−iiii−ii−iii−i−iii−i−i-1-111-1-111-1-111-1-111
χ201-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−i−iii−i−iii−ii−ii−i−iii−i−iii11-1-111-1-111-1-111-1-1
χ211-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−ii−ii−i−i−iii−i−iiii−ii−i−i−iii−i−iii11-1-111-1-1-1-111-1-111
χ221-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii−i−iii−i−iii−ii−iiii−i−iii−i−i-1-111-1-11111-1-111-1-1
χ231-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−iii−i−iii−i−ii−ii−i−i−iii−i−iii-1-111-1-11111-1-111-1-1
χ241-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−ii−iiii−i−iii−i−i−ii−iiii−i−iii−i−i11-1-111-1-1-1-111-1-111
χ251-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11-1-11111-1-11-1-11−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ261-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-111-1-1-11111-1-1-111-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ271-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1-1111-1-1-1-1111-1-11−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ281-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-111-1-1-1-111-111-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ291-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1-1111-1-1-1-1111-1-11ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ301-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-111-1-1-1-111-111-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ311-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11-1-11111-1-11-1-11ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ321-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-111-1-1-11111-1-1-111-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
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χ352222222222222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22222-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
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χ382222222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222000000000000000000000000-2-2-2-2000000002222000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
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χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-222-2-20000000000000000000000002i2i−2i−2i00000000−2i−2i2i2i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-222-2-2000000000000000000000000−2i−2i2i2i000000002i2i−2i−2i000000000000000000000000
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χ4622-22-2-22-22i2i−2i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22-22i−2i2i−2i00000000000000000000000000000000000000000000000000000000−2i2i−2i2i-22-22
χ4722-22-2-22-22i2i−2i−2i2i−2i2i−2i2-22-2-22-222i−2i2i−2i−2i2i−2i2i-22-22−2i2i−2i2i00000000000000002-22-22i−2i2i−2i0000000000000000000000000000000000000000
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χ5222-22-2-22-22i2i−2i−2i2i−2i2i−2i-22-22-222-2−2i2i−2i2i−2i2i2i−2i2-2-22−2i2i2i−2i0000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000
χ5322-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000000000000000000000000000002i−2i2i−2i-22-22
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χ5522-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222i−2i2i−2i00000000000000002-22-2−2i2i−2i2i0000000000000000000000000000000000000000
χ5622-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222i−2i2i−2i0000000000000000-22-222i−2i2i−2i0000000000000000000000000000000000000000
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χ5822-22-2-22-2−2i−2i2i2i−2i2i−2i2i-22-222-2-222i−2i2i−2i−2i2i2i−2i-222-2−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000
χ5922-22-2-22-2−2i−2i2i2i−2i2i−2i2i-22-22-222-22i−2i2i−2i2i−2i−2i2i2-2-222i−2i−2i2i00000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000
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χ622-222-2-2-222i2i−2i−2i−2i2i−2i2i2-2-222-2-222i−2i−2i2i−2i2i−2i2i2-2-222i−2i2i−2i00000000000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2
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χ692-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-222-2-22−2i2i2i−2i2i−2i2i−2i2-2-22−2i2i−2i2i000000000000000000000000000000000000000000000000000000002i−2i−2i2i-222-2
χ702-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-222-2-22−2i2i2i−2i2i−2i2i−2i2-2-22−2i2i−2i2i00000000000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22
χ712-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-22-222-2−2i2i2i−2i−2i2i−2i2i-222-22i−2i2i−2i00000000000000002i−2i−2i2i2-2-220000000000000000000000000000000000000000
χ722-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-22-222-2−2i2i2i−2i−2i2i−2i2i-222-22i−2i2i−2i0000000000000000−2i2i2i−2i-222-20000000000000000000000000000000000000000
χ732-222-2-2-22−2i−2i2i2i2i−2i2i−2i-222-22-22-22i−2i−2i2i2i−2i−2i2i-22-22−2i2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000
χ742-222-2-2-22−2i−2i2i2i2i−2i2i−2i-222-22-22-22i−2i−2i2i2i−2i−2i2i-22-22−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000
χ752-222-2-2-22−2i−2i2i2i2i−2i2i−2i-222-2-22-222i−2i−2i2i−2i2i2i−2i2-22-22i−2i−2i2i00000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000000000
χ762-222-2-2-22−2i−2i2i2i2i−2i2i−2i-222-2-22-222i−2i−2i2i−2i2i2i−2i2-22-22i−2i−2i2i0000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000000000
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χ822-2-2222-2-22222-2-2-2-2-2-222-2-2-2-2-2-22222-2-22222-2-222000000000000000000000000−2i2i−2i2i000000002i−2i2i−2i000000000000000000000000
χ832-2-2222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-2-2-222222200000000000000000000000000000000000000002-2-22-222-20000000000000000
χ842-2-2222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-2-2-22222220000000000000000000000000000000000000000-222-22-2-220000000000000000
χ852-2-2222-2-2-2-2-2-22222-2-222222222-2-222-2-2-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ862-2-2222-2-2-2-2-2-22222-2-222222222-2-222-2-2-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ872-2-2222-2-2-2-2-2-22222-2-222-2-2-2-222-2-2-2-222222222-2-20000000000000000000000002-2-2200000000-222-2000000000000000000000000
χ882-2-2222-2-2-2-2-2-22222-2-222-2-2-2-222-2-2-2-222222222-2-2000000000000000000000000-222-2000000002-2-22000000000000000000000000
χ89444-44-4-4-44-44-444-4-40000000000000000000000000022−220022−220022−220022−22000000000000000000000000000000000000000000000000
χ90444-44-4-4-44-44-444-4-400000000000000000000000000−222200−222200−222200−2222000000000000000000000000000000000000000000000000
χ91444-44-4-4-4-44-44-4-444000000000000000000000000002i2−2i2002i2−2i200−2i22i200−2i22i2000000000000000000000000000000000000000000000000
χ92444-44-4-4-4-44-44-4-44400000000000000000000000000−2i22i200−2i22i2002i2−2i2002i2−2i2000000000000000000000000000000000000000000000000
χ9344-4-4-44-444i−4i−4i4i4i−4i−4i4i0000000000000000000000002−2i−2+2i002−2i−2+2i002+2i−2−2i002+2i−2−2i00000000000000000000000000000000000000000000000000
χ9444-4-4-44-444i−4i−4i4i4i−4i−4i4i000000000000000000000000−2+2i2−2i00−2+2i2−2i00−2−2i2+2i00−2−2i2+2i00000000000000000000000000000000000000000000000000
χ9544-4-4-44-44−4i4i4i−4i−4i4i4i−4i0000000000000000000000002+2i−2−2i002+2i−2−2i002−2i−2+2i002−2i−2+2i00000000000000000000000000000000000000000000000000
χ9644-4-4-44-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000−2−2i2+2i00−2−2i2+2i00−2+2i2−2i00−2+2i2−2i00000000000000000000000000000000000000000000000000
χ974-44-4-444-44i−4i−4i4i−4i4i4i−4i0000000000000000000000002−2i−2+2i00−2+2i2−2i002+2i−2−2i00−2−2i2+2i00000000000000000000000000000000000000000000000000
χ984-44-4-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000−2+2i2−2i002−2i−2+2i00−2−2i2+2i002+2i−2−2i00000000000000000000000000000000000000000000000000
χ994-44-4-444-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000002+2i−2−2i00−2−2i2+2i002−2i−2+2i00−2+2i2−2i00000000000000000000000000000000000000000000000000
χ1004-44-4-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000−2−2i2+2i002+2i−2−2i00−2+2i2−2i002−2i−2+2i00000000000000000000000000000000000000000000000000
χ1014-4-4-44-4444-44-4-4-4440000000000000000000000000022−2200−22220022−2200−2222000000000000000000000000000000000000000000000000
χ1024-4-4-44-4444-44-4-4-44400000000000000000000000000−22220022−2200−22220022−22000000000000000000000000000000000000000000000000
χ1034-4-4-44-444-44-4444-4-4000000000000000000000000002i2−2i200−2i22i200−2i22i2002i2−2i2000000000000000000000000000000000000000000000000
χ1044-4-4-44-444-44-4444-4-400000000000000000000000000−2i22i2002i2−2i2002i2−2i200−2i22i2000000000000000000000000000000000000000000000000

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