Finite Group Databasebeta

← Group #211289

Character table — Group #211289

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444444444444444444444444448888888888888888888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-111-1-111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111
χ911111111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
χ1411111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111
χ1511111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ171-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−iiiii−i−i−i−i11-1-11-111-1-1i−i11-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-11-11-1i−ii−ii−i1-1
χ181-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−iiiii−i−i−i−i11-1-11-111-1-1i−i11-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111-11-11−ii−ii−ii-11
χ191-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−iiiii−i−i−i−i11-1-11-111-1-1i−i-1-111−i−iii-1-111−i−iii−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-11-1-11i−i−ii−ii-11
χ201-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−iiiii−i−i−i−i11-1-11-111-1-1i−i-1-111−i−iii-1-111−i−iii−i−i−i−iiiii-1-1-1-11111−i−iii-1-111-111-1−iii−ii−i1-1
χ211-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−i−i−i−i−iiiii-1-1111-1-1-111i−i11-1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-1-11-11−ii−iii−i1-1
χ221-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−i−i−i−i−iiiii-1-1111-1-1-111i−i11-1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-1-1111-11-1i−ii−i−ii-11
χ231-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−i−i−i−i−iiiii-1-1111-1-1-111i−i-1-111−i−iii-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1-111-1−iii−i−ii-11
χ241-11-1-111-1ii−i−i1-1ii−i−i1-11-11-1i−i−i−i−i−iiiii-1-1111-1-1-111i−i-1-111−i−iii-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−iii-1-1111-1-11i−i−iii−i1-1
χ251-11-1-111-1−i−iii1-1−i−iii1-11-11-1−iiiiii−i−i−i−i-1-1111-1-1-111−ii11-1-1−i−iii11-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111ii−i−i-1-1111-11-1−ii−iii−i-11
χ261-11-1-111-1−i−iii1-1−i−iii1-11-11-1−iiiiii−i−i−i−i-1-1111-1-1-111−ii11-1-1−i−iii11-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iii11-1-1-11-11i−ii−i−ii1-1
χ271-11-1-111-1−i−iii1-1−i−iii1-11-11-1−iiiiii−i−i−i−i-1-1111-1-1-111−ii-1-111ii−i−i-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-1111-1-11−iii−i−ii1-1
χ281-11-1-111-1−i−iii1-1−i−iii1-11-11-1−iiiiii−i−i−i−i-1-1111-1-1-111−ii-1-111ii−i−i-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1-111-1i−i−iii−i-11
χ291-11-1-111-1−i−iii1-1−i−iii1-11-11-1−ii−i−i−i−iiiii11-1-11-111-1-1−ii11-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111-11-11i−ii−ii−i-11
χ301-11-1-111-1−i−iii1-1−i−iii1-11-11-1−ii−i−i−i−iiiii11-1-11-111-1-1−ii11-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-11-11-1−ii−ii−ii1-1
χ311-11-1-111-1−i−iii1-1−i−iii1-11-11-1−ii−i−i−i−iiiii11-1-11-111-1-1−ii-1-111ii−i−i-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111ii−i−i-1-111-111-1i−i−ii−ii1-1
χ321-11-1-111-1−i−iii1-1−i−iii1-11-11-1−ii−i−i−i−iiiii11-1-11-111-1-1−ii-1-111ii−i−i-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111−i−iii11-1-11-1-11−iii−ii−i-11
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χ34222222222222222222-2-2-2-222-2-2-2-222-2-222-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
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χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000220000-2-200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000220000-2-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ3922222222-2-2-2-222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-2222222-2-2-2-2-2-2220000000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-222222222-2-222000000000000-2-20000-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-222222222-2-222000000000000-2-20000-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
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χ452222-2-2-2-22-22-2222-22-20000-2-2002-2002-2002-22-2000000002−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−200000000000000000000
χ462222-2-2-2-22-22-2222-22-20000-2-2002-2002-2002-22-200000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−2200000000000000000000
χ472222-2-2-2-22-22-2222-22-20000-2-200-2200-2200-22-22000000002−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−2200000000000000000000
χ482222-2-2-2-22-22-2222-22-20000-2-200-2200-2200-22-2200000000−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−200000000000000000000
χ492222-2-2-2-22-22-2-2-2-22-2200002200002i−2i002i−2i0000002i−2i2i−2i002−22−22−22−2−22−22−22−22i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000000000
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χ542222-2-2-2-2-22-2222-22-220000-2-2002-2002-200-22-2200000000−22−222−22−2−22−222−22−2−22−22−22−222−22−22−22−200000000000000000000
χ552222-2-2-2-2-22-2222-22-220000-2-200-2200-22002-22-2000000002−22−2−22−222−22−2−22−22−22−22−22−222−22−22−22−200000000000000000000
χ562222-2-2-2-2-22-2222-22-220000-2-200-2200-22002-22-200000000−22−222−22−2−22−222−22−22−22−22−22−2−22−22−22−2200000000000000000000
χ572222-2-2-2-2-22-22-2-22-22-200002200002i−2i002i−2i000000−2i2i−2i2i002−22−2−22−22−22−222−22−2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000000000
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χ812-22-2-222-22i2i−2i−2i-22−2i−2i2i2i-22-22-222i−2i0000000000002-20000−2i2i000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ822-22-2-222-22i2i−2i−2i-22−2i−2i2i2i-22-22-222i−2i0000000000002-20000−2i2i0000000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ832-22-2-222-2−2i−2i2i2i2-2−2i−2i2i2i-22-222-22i−2i2i2i−2i−2i−2i−2i2i2i-2-222-2222-2-22i−2i0000000000000000000000000000000000000000000000000000
χ842-22-2-222-2−2i−2i2i2i2-2−2i−2i2i2i-22-222-22i−2i−2i−2i2i2i2i2i−2i−2i22-2-2-22-2-2222i−2i0000000000000000000000000000000000000000000000000000
χ852-22-2-222-2−2i−2i2i2i-222i2i−2i−2i2-22-2-222i−2i000000000000-220000−2i2i22-2-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000000000
χ862-22-2-222-2−2i−2i2i2i-222i2i−2i−2i2-22-2-222i−2i000000000000-220000−2i2i-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000000000000000
χ872-22-2-222-2−2i−2i2i2i-222i2i−2i−2i-22-22-22−2i2i0000000000002-200002i−2i000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ882-22-2-222-2−2i−2i2i2i-222i2i−2i−2i-22-22-22−2i2i0000000000002-200002i−2i0000000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ8944-4-4-44-4400000000004-4-44000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ9044-4-4-44-4400000000004-4-4400000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ9144-4-4-44-440000000000-444-40000000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ9244-4-4-44-440000000000-444-4000000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ934-4-4444-4-4000000000044-4-40000000000000000000000000000000000000000000000000000000022−22−22220000000000000000
χ944-4-4444-4-4000000000044-4-400000000000000000000000000000000000000000000000000000000−222222−220000000000000000
χ954-4-4444-4-40000000000-4-4440000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ964-4-4444-4-40000000000-4-444000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ9788-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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