Finite Group Databasebeta

← Group #375793

Character table — Group #375793

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222444444442222444488888888888888882222444488888888222244444444444444444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ11111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ12111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111
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χ1811111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-111-1-111
χ1911111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-11111-1-111-1-1−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111
χ2011111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i-1-1-1-1-1-111-1-1111111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ2111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii1111-1-111-1-111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ2211111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii11-1-1-1-11111-1-1-1-111−i−iiiii−i−iii−i−iii−i−i−i−iii−i−iii-1-11111-1-1
χ2311111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1
χ2411111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii-1-1-1-111-1-111-1-11111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i1111-1-111-1-111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i11-1-1-1-11111-1-1-1-111ii−i−i−i−iii−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−iii−i−i−i−iii−i−iii-1-11111-1-1
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i-1-1-1-111-1-111-1-11111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii111111-1-111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii-1-111-1-11111-1-111-1-1ii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iii-1-111-1-111
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii-1-1-1-1-1-111-1-1111111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
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χ342222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-22222-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2-2-22222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-2-2-222222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i2222-2-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4122-222-2-2-22i−2i2i2i−2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32-200002i−2i0000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000000000002−2i2−i22−2i2−i2
χ4222-222-2-2-22i−2i2i2i−2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32-200002i−2i000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000000000−22−i2i2−22−i2i2
χ4322-222-2-2-22i−2i2i2i−2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3-220000−2i2i0000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000000000002−2i2−i2−22−i2i2
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χ4722-222-2-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32-200002i−2i0000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000000000−22−i2i2−22−i2i2
χ4822-222-2-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32-200002i−2i000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000000000002−2i2−i22−2i2−i2
χ4922-222-2-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2-20000−2i2i0000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000000000−22i2−i2−22i2−i2
χ5022-222-2-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2-20000−2i2i000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000000000002−2−i2i22−2−i2i2
χ5122-222-2-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-2200002i−2i0000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000000000−22i2−i22−2−i2i2
χ5222-222-2-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-2200002i−2i000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000000000002−2−i2i2−22i2−i2
χ5322-222-2-2-2−2i2i−2i−2i2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ-2200002i−2i0000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000000000002−2−i2i2−22i2−i2
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χ5622-222-2-2-2−2i2i−2i−2i2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2-20000−2i2i000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000000000−22i2−i2−22i2−i2
χ572-2-22-22-22222-22-2-2-22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i0000000000002i−2i2i−2i000000002-22-20000000000000000000000002i−2i2i−2i00000000
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χ782-2-2-22-22222-22-22-2-2-222-22-2-222i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i−2i2i0000-220000000000-220000000000−2i2i−2i2i00000000000000000000
χ792-2-2-22-22222-22-22-2-2-222-22-2-22−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i00002-200000000002-20000000000−2i2i−2i2i00000000000000000000
χ802-2-2-22-22222-22-22-2-2-222-22-2-22−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i0000-220000000000-2200000000002i−2i2i−2i00000000000000000000
χ812-2-2-22-222-2-22-22-2222-2-222-2-222-22-2-22-220000000000000000-222-200002-20000000000-2200000000002-2-2200000000000000000000
χ822-2-2-22-222-2-22-22-2222-2-222-2-222-22-2-22-220000000000000000-222-20000-2200000000002-20000000000-222-200000000000000000000
χ832-2-2-22-222-2-22-22-2222-2-222-2-22-22-222-22-200000000000000002-2-2200002-20000000000-220000000000-222-200000000000000000000
χ842-2-2-22-222-2-22-22-2222-2-222-2-22-22-222-22-200000000000000002-2-220000-2200000000002-200000000002-2-2200000000000000000000
χ852-2-2-22-222-2-22-22-222-222-2-222-22-22-2-22-2200000000000000002-2-22000000002-2-220000000000000000000000002-2-22000000000000
χ862-2-2-22-222-2-22-22-222-222-2-222-22-22-2-22-2200000000000000002-2-2200000000-222-2000000000000000000000000-222-2000000000000
χ872-2-2-22-222-2-22-22-222-222-2-222-2-22-222-22-20000000000000000-222-2000000002-2-22000000000000000000000000-222-2000000000000
χ882-2-2-22-222-2-22-22-222-222-2-222-2-22-222-22-20000000000000000-222-200000000-222-20000000000000000000000002-2-22000000000000
χ89444-4-4-4-4444-4-4-4-44444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4-4-4444-4-4-4-444-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ91444-4-4-4-44-4-44444-4-444-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ92444-4-4-4-44-4-44444-4-4-4-444-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-444-44i−4i−4i−4i4i4i4i−4i000000000000000000000000004-44i−4i0000000000000000000000000000000000000000000000000000000000
χ9444-4-4-444-44i−4i−4i−4i4i4i4i−4i00000000000000000000000000-44−4i4i0000000000000000000000000000000000000000000000000000000000
χ9544-4-4-444-4−4i4i4i4i−4i−4i−4i4i000000000000000000000000004-4−4i4i0000000000000000000000000000000000000000000000000000000000
χ9644-4-4-444-4−4i4i4i4i−4i−4i−4i4i00000000000000000000000000-444i−4i0000000000000000000000000000000000000000000000000000000000
χ974-444-4-44-44i−4i4i−4i−4i4i−4i4i00000000000000004ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ0000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-44-44i−4i4i−4i−4i4i−4i4i0000000000000000−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ0000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-44-4−4i4i−4i4i4i−4i4i−4i00000000000000004ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ30000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-44-4−4i4i−4i4i4i−4i4i−4i0000000000000000−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ30000000000000000000000000000000000000000000000000000000000000000
χ1014-44-444-4-44i−4i−4i4i4i−4i−4i4i000000004ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-444-4-44i−4i−4i4i4i−4i−4i4i00000000−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-44-444-4-4−4i4i4i−4i−4i4i4i−4i000000004ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-44-444-4-4−4i4i4i−4i−4i4i4i−4i00000000−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ3000000000000000000000000000000000000000000000000000000000000000000000000

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