Finite Group Databasebeta

← Group #155993

Character table — Group #155993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111111111111111111111444444444444444444444444888888888888888888888888888888888888888888888888
order12222222222222222222222222222222444444444444444444444444444444444444444444444444444444444444444444444444
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
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
χ1711111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-111-1-111-1-1ii−i−iii−i−i
χ1811111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1ii−i−i11-1-1−i−iii-1-111−i−iii-1-111-1-111-1-111−i−iii−i−iii
χ1911111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111−i−iii-1-111ii−i−i11-1-1ii−i−i11-1-1-1-111-1-111−i−iii−i−iii
χ2011111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111−i−iii-1-111−i−iii-1-111−i−iii-1-11111-1-111-1-1ii−i−iii−i−i
χ2111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-11111-1-1-1-111ii−i−i−i−iii
χ2211111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1−i−iii-1-111−i−iii-1-111ii−i−i11-1-1-1-11111-1-1−i−iiiii−i−i
χ2311111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−iii-1-111ii−i−i11-1-1ii−i−i11-1-1−i−iii-1-111-1-11111-1-1−i−iiiii−i−i
χ2411111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-111-1-1-1-111ii−i−i−i−iii
χ2511111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-1-11111-1-111-1-1−i−iii−i−iii
χ2611111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111ii−i−i-1-111−i−iii11-1-1−i−iii11-1-1-1-111-1-111ii−i−iii−i−i
χ2711111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1−i−iii11-1-1ii−i−i-1-111ii−i−i-1-111-1-111-1-111ii−i−iii−i−i
χ2811111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-111-1-111-1-1−i−iii−i−iii
χ2911111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-111-1-1-1-111−i−iiiii−i−i
χ3011111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iii−i−i-1-111−i−iii11-1-1−i−iii11-1-1ii−i−i-1-111-1-11111-1-1ii−i−i−i−iii
χ3111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1ii−i−i-1-111ii−i−i-1-111−i−iii11-1-1-1-11111-1-1ii−i−i−i−iii
χ3211111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-11111-1-1-1-111−i−iiiii−i−i
χ33222222-2-2-2-2-2222222-2-2-2-22-2-22-2-2-2-22-220000000022-2-222-2-20000000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000000000000000
χ34222222-2-2-2-2-2222222-2-2-2-22-2-22-2-2-2-22-220000000022-2-222-2-2000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000
χ35222222-2-2-2-2-2222222-2-2-2-22-2-22-2-2-2-22-2200000000-2-222-2-2220000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000000000000000
χ36222222-2-2-2-2-2222222-2-2-2-22-2-22-2-2-2-22-2200000000-2-222-2-222000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000000000000000
χ37222222-2-2-2-2-2-2-2-2-2-2-222222-2-2-222222-2-20000000022-2-2-2-2220000000000002i−2i−2i2i00002i−2i−2i2i00000000000000000000000000000000
χ38222222-2-2-2-2-2-2-2-2-2-2-222222-2-2-222222-2-20000000022-2-2-2-222000000000000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000000000000000
χ39222222-2-2-2-2-2-2-2-2-2-2-222222-2-2-222222-2-200000000-2-22222-2-20000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000000000000000
χ40222222-2-2-2-2-2-2-2-2-2-2-222222-2-2-222222-2-200000000-2-22222-2-2000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000000000000000000000
χ41222-2-2-2222-2-2222-2-2-2222-22-2-2-22-2-2-2-222000000000000000022-2-222-2-200000000000000002i−2i2i−2i000000002i−2i2i−2i0000000000000000
χ42222-2-2-2222-2-2222-2-2-2222-22-2-2-22-2-2-2-222000000000000000022-2-222-2-20000000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000000000
χ43222-2-2-2222-2-2222-2-2-2222-22-2-2-22-2-2-2-2220000000000000000-2-222-2-22200000000000000002i−2i2i−2i00000000−2i2i−2i2i0000000000000000
χ44222-2-2-2222-2-2222-2-2-2222-22-2-2-22-2-2-2-2220000000000000000-2-222-2-2220000000000000000−2i2i−2i2i000000002i−2i2i−2i0000000000000000
χ45222-2-2-2222-2-2-2-2-2222-2-2-222-2-22-2222-22-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000002-2-2200000000−2i2i2i−2i0000000000000000
χ46222-2-2-2222-2-2-2-2-2222-2-2-222-2-22-2222-22-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000-222-2000000002i−2i−2i2i0000000000000000
χ47222-2-2-2222-2-2-2-2-2222-2-2-222-2-22-2222-22-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000002-2-22000000002i−2i−2i2i0000000000000000
χ48222-2-2-2222-2-2-2-2-2222-2-2-222-2-22-2222-22-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000-222-200000000−2i2i2i−2i0000000000000000
χ4922-22-2-22-2-22-222-222-222-2-2-22-2-2-222-222-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000002-22-200002i−2i2i−2i0000
χ5022-22-2-22-2-22-222-222-222-2-2-22-2-2-222-222-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000-22-220000−2i2i−2i2i0000
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χ5322-22-2-22-2-22-2-2-22-2-22-2-222-22-222-2-2222222-2-2-2-2220000000000000000000000000000000000000000000000002-2-2200002-2-220000
χ5422-22-2-22-2-22-2-2-22-2-22-2-222-22-222-2-2222222-2-2-2-222000000000000000000000000000000000000000000000000-222-20000-222-20000
χ5522-22-2-22-2-22-2-2-22-2-22-2-222-22-222-2-22222-2-22222-2-20000000000000000000000000000000000000000000000002-2-220000-222-20000
χ5622-22-2-22-2-22-2-2-22-2-22-2-222-22-222-2-22222-2-22222-2-2000000000000000000000000000000000000000000000000-222-200002-2-220000
χ572-22-22-2-22-22-22-222-222-22-2-2-22-2-22-2222-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000002-22-200002i−2i2i−2i
χ582-22-22-2-22-22-22-222-222-22-2-2-22-2-22-2222-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000-22-220000−2i2i−2i2i
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χ782-2-2-2-2222-2-2-2-222-2222-2-22222-222-2-22-2-2000000002-22-2-22-2200000000−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000000000000000
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χ802-2-2-2-2222-2-2-2-222-2222-2-22222-222-2-22-2-200000000-22-222-22-200000000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000000000000000
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χ872-2-2-2-22-2-2222-222-222-222-22-2-2-2-2-22222-2−2i2i2i−2i2i−2i−2i2i2-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000
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χ1034-4-444-444-4444-4-4-444-44444-4-4-4-44-4-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-444-444-444-4444-4-44-4-4-44-4-444-444-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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