Finite Group Databasebeta

← Group #205356

Character table — Group #205356

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-111-1-1
χ1311111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-11111-1-1
χ1511111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1611111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ171-1-11-1-11111-1-111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1-11-11-11-1i−ii−i
χ181-1-11-1-11111-1-111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−i−iii−i−iii-11-11-11-11−ii−ii
χ191-1-11-1-11111-1-111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i-111-11-1-11−ii−ii
χ201-1-11-1-11111-1-111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iii−i−iii1-1-11-111-1i−ii−i
χ211-1-11-1-11111-1-111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−iii−i−i1-1-11-111-1−ii−ii
χ221-1-11-1-11111-1-111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii-111-11-1-11i−ii−i
χ231-1-11-1-11111-1-111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i-11-11-11-11i−ii−i
χ241-1-11-1-11111-1-111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii1-11-11-11-1−ii−ii
χ251-1-11-1-111-1-11111-1-1-11111-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii1-11-1-11-11i−i−ii
χ261-1-11-1-111-1-11111-1-1-11111-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-11-111-11-1−iii−i
χ271-1-11-1-111-1-11111-1-1-11111-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-111-1-111-1−iii−i
χ281-1-11-1-111-1-11111-1-1-11111-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i1-1-111-1-11i−i−ii
χ291-1-11-1-111-1-11111-1-1-11111-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iii1-1-111-1-11−iii−i
χ301-1-11-1-111-1-11111-1-1-11111-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-111-1-111-1i−i−ii
χ311-1-11-1-111-1-11111-1-1-11111-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-11-111-11-1i−i−ii
χ321-1-11-1-111-1-11111-1-1-11111-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i1-11-1-11-11−iii−i
χ332222222222222222222-2-2-2-2222-2-222-2-222-2-222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000
χ342222222222222222222-2-2-2-22-2-222-2-222-2-222-2-222-2-2-2-2-2-20000000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-22222-2000000000000000022-2-2-2-2000000000000000022-2-222-2-222-2-222-2-200000000000000000000
χ36222222222222-2-2-2-2-2-2-22222-2000000000000000022-2-2-2-20000000000000000-2-222-2-222-2-222-2-22200000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-222222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-22222−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3922222222-2-2-2-2222-2-2-2-2-2-2-2-2222-2-222-2-2-2-222-2-22222-2-2220000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2222-2-2-2-2-2-2-2-22-2-222-2-22222-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-222222222-20000000000000000-2-2-2-222000000000000000022-2-222-2-2-2-222-2-22200000000000000000000
χ4222222222-2-2-2-2-2-2-222222222-20000000000000000-2-2-2-2220000000000000000-2-222-2-22222-2-222-2-200000000000000000000
χ4322222222-2-2-2-2-2-2-22222-2-2-2-2-200000000000000002222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-22222-2-2-2-2-200000000000000002222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ4522-222-2-2-22-22-22-222-22-20000-2002-2002-2002-2002-20000002−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−200000000000000000000
χ4622-222-2-2-22-22-22-222-22-20000-2002-2002-2002-2002-2000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−2200000000000000000000
χ4722-222-2-2-22-22-22-222-22-20000-200-2200-2200-2200-220000002−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−2200000000000000000000
χ4822-222-2-2-22-22-22-222-22-20000-200-2200-2200-2200-22000000−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−200000000000000000000
χ4922-222-2-2-22-22-2-22-2-22-22000022i−2i002i−2i002i−2i002i−2i00000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i22−2−222−2−222−2−222−2−2200000000000000000000
χ5022-222-2-2-22-22-2-22-2-22-22000022i−2i002i−2i002i−2i002i−2i00000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−222−2−222−2−222−2−222−200000000000000000000
χ5122-222-2-2-22-22-2-22-2-22-2200002−2i2i00−2i2i00−2i2i00−2i2i00000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−222−2−222−2−222−2−222−200000000000000000000
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χ5322-222-2-2-2-22-222-22-22-220000-2002-2002-200-2200-220000002−22−22−22−2−22−22−22−222−22−22−22−2−22−22−22−2200000000000000000000
χ5422-222-2-2-2-22-222-22-22-220000-2002-2002-200-2200-22000000−22−22−22−222−22−22−22−2−22−22−22−222−22−22−22−200000000000000000000
χ5522-222-2-2-2-22-222-22-22-220000-200-2200-22002-2002-20000002−22−22−22−2−22−22−22−22−22−22−22−222−22−22−22−200000000000000000000
χ5622-222-2-2-2-22-222-22-22-220000-200-2200-22002-2002-2000000−22−22−22−222−22−22−22−22−22−22−22−2−22−22−22−2200000000000000000000
χ5722-222-2-2-2-22-22-22-22-22-2000022i−2i002i−2i00−2i2i00−2i2i00000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i22−2−222−2−22−222−2−222−200000000000000000000
χ5822-222-2-2-2-22-22-22-22-22-2000022i−2i002i−2i00−2i2i00−2i2i00000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−222−2−222−22−2−222−2−2200000000000000000000
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χ944-4-4-4444-4000000000004-4-440000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ954-4-4-4444-400000000000-444-4000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ964-4-4-4444-400000000000-444-400000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ9788-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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