Finite Group Databasebeta

← Group #360951

Character table — Group #360951

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111111111111111111111444444444444444444444444888888888888888888888888888888888888888888888888
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
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
χ911111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ181111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ191111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ201111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ211111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ231111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ241111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
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χ3522222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000000000002-22-2-22-22
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χ5522-22-2-22-22-22-22-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i2i00000000-2-2222i2i−2i−2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000
χ5622-22-2-22-22-22-22-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i2i00000000-2-2222i2i−2i−2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000
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χ642-22-22-22-22-22-2-22-22−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i2-22-2000000000000000000000000−2ζ2ζ−2ζ32ζ30000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ652-2-2222-2-222-2-2-2-2222-2-22-2-222222-2-22-2-200000000000000002-22-22-22-22i−2i2i−2i000000002i−2i2i−2i00000000000000000000000000000000
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χ742-2-2-2-22222222-2-2-2-22-2-2222-2-2-2-22-2-22222-22-22-22-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ752-2-2-2-22222222-2-2-2-22-2-2222-2-2-2-22-2-2222-22-22-22-222i−2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
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χ792-2-2-2-22222222-2-2-2-2-222-2-2-22222-222-2-2-2-22-222-22-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ802-2-2-2-22222222-2-2-2-2-222-2-2-22222-222-2-2-2-22-222-22-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000
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χ882-2-2-2-2222-2-2-2-22222-222-2-2-2-2-2222-2-2222-222-22-2-22000000000000000000000000000000000000000000000000-222-22-2-2200000000
χ89444-4-44-4-4-4-444-4-4444444-4-444-4-4-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-44-4-4-4-444-4-444-4-4-4-444-4-4444444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-44-4-44-4-44-44-44-444i4i−4i−4i4i−4i−4i4i4i−4i−4i−4i4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-44-4-44-4-44-44-44-44−4i−4i4i4i−4i4i4i−4i−4i4i4i4i−4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4-444-4-444-4-444i4i−4i−4i−4i4i−4i4i−4i4i4i4i−4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-444-4-444-4-44−4i−4i4i4i4i−4i4i−4i4i−4i−4i−4i4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-44-444-4-444-44i4i−4i−4i−4i4i4i−4i−4i4i−4i−4i4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-44-444-4-444-4−4i−4i4i4i4i−4i−4i4i4i−4i4i4i−4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-444-4-44-444-44i−4i4i−4i−4i4i4i−4i4i−4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-444-4-44-444-4−4i4i−4i4i4i−4i−4i4i−4i4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-44-444-44-4-444i−4i4i−4i−4i4i−4i4i4i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-44-444-44-4-44−4i4i−4i4i4i−4i4i−4i−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-44-4-44-444-44-44i−4i4i−4i4i−4i4i−4i−4i4i−4i4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-44-4-44-444-44-4−4i4i−4i4i−4i4i−4i4i4i−4i4i−4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4444-4-4-4-44444-4-44-4-44-4-4-4-444-444-444000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4444-4-4-4-44444-4-4-444-44444-4-44-4-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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