Finite Group Databasebeta

← Group #225621

Character table — Group #225621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1711-1-111-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-111-1-111-1-1ii−i−iii−i−i111-1-111-1-11111-1-1-1-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ1811-1-111-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-111-1-111-1-1−i−iii−i−iii111-1-111-1-11111-1-1-1-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ1911-1-111-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-111-1-111ii−i−iii−i−i111-1-111-1-11111-1-1-1-1i−ii−i-11-11ii−i−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ2011-1-111-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-111-1-111−i−iii−i−iii111-1-111-1-11111-1-1-1-1−ii−ii-11-11−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i
χ2111-1-111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111-111-1-111-1-1ii−i−i−i−iii111-1-1-1-111-1-1-1-11111i−i−ii1-11-1ii−i−i−i−iii-1-111-1-111i−ii−i−ii−ii
χ2211-1-111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111-111-1-111-1-1−i−iiiii−i−i111-1-1-1-111-1-1-1-11111−iii−i1-11-1−i−iiiii−i−i-1-111-1-111−ii−iii−ii−i
χ2311-1-111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111-1-1-111-1-111ii−i−i−i−iii111-1-1-1-111-1-1-1-11111i−i−ii-11-11ii−i−i−i−iii11-1-111-1-1−ii−iii−ii−i
χ2411-1-111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111-1-1-111-1-111−i−iiiii−i−i111-1-1-1-111-1-1-1-11111−iii−i-11-11−i−iiiii−i−i11-1-111-1-1i−ii−i−ii−ii
χ2511-1-111-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-1-111-1-1-1-111ii−i−iii−i−i1-1-11111-1-1-1-1-1-11111i−ii−i1-1-11−i−iii−i−iii11-1-1-1-111i−i−iii−i−ii
χ2611-1-111-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-1-111-1-1-1-111−i−iii−i−iii1-1-11111-1-1-1-1-1-11111−ii−ii1-1-11ii−i−iii−i−i11-1-1-1-111−iii−i−iii−i
χ2711-1-111-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-1-1-1-11111-1-1ii−i−iii−i−i1-1-11111-1-1-1-1-1-11111i−ii−i-111-1−i−iii−i−iii-1-11111-1-1−iii−i−iii−i
χ2811-1-111-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-1-1-1-11111-1-1−i−iii−i−iii1-1-11111-1-1-1-1-1-11111−ii−ii-111-1ii−i−iii−i−i-1-11111-1-1i−i−iii−i−ii
χ2911-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-111-1-1-1-111ii−i−i−i−iii1-1-111-1-1111111-1-1-1-1i−i−ii1-1-11−i−iiiii−i−i-1-11111-1-1i−i−ii−iii−i
χ3011-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-111-1-1-1-111−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1−iii−i1-1-11ii−i−i−i−iii-1-11111-1-1−iii−ii−i−ii
χ3111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-1-1-11111-1-1ii−i−i−i−iii1-1-111-1-1111111-1-1-1-1i−i−ii-111-1−i−iiiii−i−i11-1-1-1-111−iii−ii−i−ii
χ3211-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-1-1-11111-1-1−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1−iii−i-111-1ii−i−i−i−iii11-1-1-1-111i−i−ii−iii−i
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χ3522222222222-2-2-2-2200000000-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-20000222200000000-2-2220000000000000000000000000000
χ3622222222222-2-2-2-2200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-2000022220000000022-2-20000000000000000000000000000
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χ3822222222-2-2-22222-22222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000000002222000000000000000000000000
χ3922222222-2-2-22222-2-2-2-2-2-2-2-2-200000000-22222-2-2-2-200000000-222220000000000000000-2-222000000000000000000000000
χ4022222222-2-2-22222-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-22222000000000000000022-2-2000000000000000000000000
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χ42222-2-2-22-22-2-20000222−2−222−2−22i2i−2i−2i2i2i−2i−2i000000000-22-22−2i2i−2i2i02−22−20000i2i2−i2−i2i2i2−i2−i200000000−22−22−i2i2−i2i20000000000000000
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χ5322-22-2-2-22-22-200002−2−22222−2−22i2i−2i−2i−2i−2i2i2i0000000002i−2i−2i2i-222-20−222−20000−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i22−2−220000000000000000
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χ8644-4-444-4-444-4-4-444-40000000000000000-400000000000000004000000000000000000000000000000000000000000000000
χ874-444-44-4-40000000022−22−222222−22−222222−22−222222−22−2222000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ884-444-44-4-40000000022−22−222222−22−2222−222222−22−222222−2200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ894-444-44-4-400000000−222222−22−222222−2222−22−222222−22−222200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ904-444-44-4-400000000−222222−22−222222−22−222222−22−222222−22000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ914-44-44-4-44000-44-440000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ924-44-44-4-44000-44-44000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ934-4-444-44-4000-444-40000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ944-4-444-44-4000-444-4000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ954-4-4-4-44440000000022−22−2222−222222−2222−22−2222−222222−22000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ964-4-4-4-44440000000022−22−2222−222222−22−222222−2222−22−222200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ974-4-4-4-444400000000−222222−2222−22−222222−22−2222−222222−2200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ984-4-4-4-444400000000−222222−2222−22−2222−222222−2222−22−2222000000000000000000000000002-2-22-222-200000000000000000000000000000000

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