Finite Group Databasebeta

← Group #225608

Character table — Group #225608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888222244444444444444888888888888888822444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-11111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ171-111-11-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-111-1-1-111-1-1ii−i−iii−i−i111-1-111-1-11111-1-1-1-11-1i−ii−i1-1ii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ181-111-11-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-111-1-1-111-1-1−i−iii−i−iii111-1-111-1-11111-1-1-1-11-1−ii−ii1-1−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ191-111-11-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1-1-111-1-1-111ii−i−iii−i−i111-1-111-1-11111-1-1-1-1-11i−ii−i-11ii−i−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ201-111-11-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1-1-111-1-1-111−i−iii−i−iii111-1-111-1-11111-1-1-1-1-11−ii−ii-11−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i
χ211-111-11-1-1-1-1-1111-111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1ii−i−i−i−iii111-1-1-1-111-1-1-1-111111-1i−i−ii1-1ii−i−i−i−iii-1-111-1-111i−i−iii−i−ii
χ221-111-11-1-1-1-1-1111-111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1−i−iiiii−i−i111-1-1-1-111-1-1-1-111111-1−iii−i1-1−i−iiiii−i−i-1-111-1-111−iii−i−iii−i
χ231-111-11-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111-1-111-1-1-111ii−i−i−i−iii111-1-1-1-111-1-1-1-11111-11i−i−ii-11ii−i−i−i−iii11-1-111-1-1−iii−i−iii−i
χ241-111-11-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111-1-111-1-1-111−i−iiiii−i−i111-1-1-1-111-1-1-1-11111-11−iii−i-11−i−iiiii−i−i11-1-111-1-1i−i−iii−i−ii
χ251-111-11-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-111-1-1-1-1-111ii−i−iii−i−i1-1-11111-1-1-1-1-1-11111-11i−ii−i1-1−i−iii−i−iii11-1-1-1-111−ii−iii−ii−i
χ261-111-11-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-111-1-1-1-1-111−i−iii−i−iii1-1-11111-1-1-1-1-1-11111-11−ii−ii1-1ii−i−iii−i−i11-1-1-1-111i−ii−i−ii−ii
χ271-111-11-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1-1-111-111-1-1ii−i−iii−i−i1-1-11111-1-1-1-1-1-111111-1i−ii−i-11−i−iii−i−iii-1-11111-1-1i−ii−i−ii−ii
χ281-111-11-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1-1-111-111-1-1−i−iii−i−iii1-1-11111-1-1-1-1-1-111111-1−ii−ii-11ii−i−iii−i−i-1-11111-1-1−ii−iii−ii−i
χ291-111-11-1-1-1-1-1111-11-1-1-1-11111-1-1-1-1111111-1-1-1-1-111ii−i−i−i−iii1-1-111-1-1111111-1-1-1-1-11i−i−ii1-1−i−iiiii−i−i-1-11111-1-1−iii−ii−i−ii
χ301-111-11-1-1-1-1-1111-11-1-1-1-11111-1-1-1-1111111-1-1-1-1-111−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1-11−iii−i1-1ii−i−i−i−iii-1-11111-1-1i−i−ii−iii−i
χ311-111-11-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111-1-111-111-1-1ii−i−i−i−iii1-1-111-1-1111111-1-1-1-11-1i−i−ii-11−i−iiiii−i−i11-1-1-1-111i−i−ii−iii−i
χ321-111-11-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111-1-111-111-1-1−i−iiiii−i−i1-1-111-1-1111111-1-1-1-11-1−iii−i-11ii−i−i−i−iii11-1-1-1-111−iii−ii−i−ii
χ33222222222-2-222-22-222222222000000002222-2222200000000-2-2-2-2-2000000000000-2-20000-2-2000000000000000000000000
χ34222222222-2-222-22-22222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022000022000000000000000000000000
χ35222222222-2-222-22-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200000000-22222000000000000220000-2-2000000000000000000000000
χ36222222222-2-222-22-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-22222000000000000-2-2000022000000000000000000000000
χ3722222222-222-2-22-2200000000222222220000-2000022222222-20000-2-2-2-20000000000-2-2-2-200000000000000000000000000
χ3822222222-222-2-22-2200000000222222220000-20000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000222200000000000000000000000000
χ3922222222-222-2-22-2200000000-2-2-2-2-2-2-2-20000-200002222-2-2-2-2-2000022220000000000-2-22200000000000000000000000000
χ4022222222-222-2-22-2200000000-2-2-2-2-2-2-2-20000-20000-2-2-2-22222-200002222000000000022-2-200000000000000000000000000
χ41222-2-2-22-2-2002-20202i2i−2i−2i2i2i−2i−2i22−2−222−2−22-22-202i−2i2i−2i00000000000002−22−2i2i2−i2−i2i2i2−i2−i200000000000000002−22−2i2−i2i2−i200000000
χ42222-2-2-22-2-2002-20202i2i−2i−2i2i2i−2i−2i22−2−222−2−2-22-220−2i2i−2i2i00000000000002−22−2i2i2−i2−i2i2i2−i2−i20000000000000000−22−22−i2i2−i2i200000000
χ43222-2-2-22-2-2002-20202i2i−2i−2i2i2i−2i−2i−2−222−2−2222-22-202i−2i2i−2i0000000000000−22−22−i2−i2i2i2−i2−i2i2i20000000000000000−22−22−i2i2−i2i200000000
χ44222-2-2-22-2-2002-20202i2i−2i−2i2i2i−2i−2i−2−222−2−222-22-220−2i2i−2i2i0000000000000−22−22−i2−i2i2i2−i2−i2i2i200000000000000002−22−2i2−i2i2−i200000000
χ45222-2-2-22-2-2002-2020−2i−2i2i2i−2i−2i2i2i22−2−222−2−22-22-20−2i2i−2i2i00000000000002−22−2−i2−i2i2i2−i2−i2i2i200000000000000002−22−2−i2i2−i2i200000000
χ46222-2-2-22-2-2002-2020−2i−2i2i2i−2i−2i2i2i22−2−222−2−2-22-2202i−2i2i−2i00000000000002−22−2−i2−i2i2i2−i2−i2i2i20000000000000000−22−22i2−i2i2−i200000000
χ47222-2-2-22-2-2002-2020−2i−2i2i2i−2i−2i2i2i−2−222−2−2222-22-20−2i2i−2i2i0000000000000−22−22i2i2−i2−i2i2i2−i2−i20000000000000000−22−22i2−i2i2−i200000000
χ48222-2-2-22-2-2002-2020−2i−2i2i2i−2i−2i2i2i−2−222−2−222-22-2202i−2i2i−2i0000000000000−22−22i2i2−i2−i2i2i2−i2−i200000000000000002−22−2−i2i2−i2i200000000
χ4922-2-222-2-202-200-2022−22−22−22−22-22-22-22-20000000002i−2i2i−2i2i−2i2i−2i02−22−200002−22−22−22−200000000i2−i2i2−i2i2−i2i2−i20000000000000000
χ5022-2-222-2-202-200-2022−22−22−22−22-22-22-22-2000000000−2i2i−2i2i−2i2i−2i2i02−22−200002−22−22−22−200000000−i2i2−i2i2−i2i2−i2i20000000000000000
χ5122-2-222-2-202-200-2022−22−22−22−2-22-22-22-220000000002i−2i2i−2i−2i2i−2i2i02−22−20000−22−22−22−2200000000i2−i2i2−i2−i2i2−i2i20000000000000000
χ5222-2-222-2-202-200-2022−22−22−22−2-22-22-22-22000000000−2i2i−2i2i2i−2i2i−2i02−22−20000−22−22−22−2200000000−i2i2−i2i2i2−i2i2−i20000000000000000
χ5322-2-222-2-202-200-202−22−22−22−222-22-22-22-20000000002i−2i2i−2i2i−2i2i−2i0−22−220000−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i20000000000000000
χ5422-2-222-2-202-200-202−22−22−22−222-22-22-22-2000000000−2i2i−2i2i−2i2i−2i2i0−22−220000−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i20000000000000000
χ5522-2-222-2-202-200-202−22−22−22−22-22-22-22-220000000002i−2i2i−2i−2i2i−2i2i0−22−2200002−22−22−22−200000000−i2i2−i2i2i2−i2i2−i20000000000000000
χ5622-2-222-2-202-200-202−22−22−22−22-22-22-22-22000000000−2i2i−2i2i2i−2i2i−2i0−22−2200002−22−22−22−200000000i2−i2i2−i2−i2i2−i2i20000000000000000
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χ582-222-22-2-22-2-2-2-2222000000002222-2-2-2-2000020000−2i−2i2i2i−2i−2i2i2i-20000-2-22200000000002i−2i2i−2i00000000000000000000000000
χ592-222-22-2-22-2-2-2-222200000000-2-2-2-222220000200002i2i−2i−2i−2i−2i2i2i-2000022-2-20000000000−2i2i2i−2i00000000000000000000000000
χ602-222-22-2-22-2-2-2-222200000000-2-2-2-22222000020000−2i−2i2i2i2i2i−2i−2i-2000022-2-200000000002i−2i−2i2i00000000000000000000000000
χ612-222-22-2-2-22222-2-2-22222-2-2-2-20000000022-2-2222-2-200000000-2-2-222000000000000-220000-22000000000000000000000000
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χ632-222-22-2-2-22222-2-2-2-2-2-2-222220000000022-2-22-2-22200000000-222-2-20000000000002-20000-22000000000000000000000000
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χ722-22-22-2-222002-20-20−2i−2i2i2i2i2i−2i−2i−2−22222−2−2-222-202i−2i−2i2i0000000000000−222−2i2i2−i2−i2−i2−i2i2i200000000000000002−2−22−i2i2i2−i200000000
χ732-2-2-2-22220-2200-2022−22−2−22−222-22-2-22-220000000002-2-222-2-2202−2−2200002−22−2−22−22000000002−2−222−2−220000000000000000
χ742-2-2-2-22220-2200-2022−22−2−22−222-22-2-22-22000000000-222-2-222-202−2−2200002−22−2−22−2200000000−222−2−222−20000000000000000
χ752-2-2-2-22220-2200-2022−22−2−22−22-22-222-22-20000000002-2-22-222-202−2−220000−22−222−22−2000000002−2−22−222−20000000000000000
χ762-2-2-2-22220-2200-2022−22−2−22−22-22-222-22-2000000000-222-22-2-2202−2−220000−22−222−22−200000000−222−22−2−220000000000000000
χ772-2-2-2-22220-2200-202−22−222−22−22-22-2-22-220000000002-2-222-2-220−222−20000−22−222−22−200000000−222−2−222−20000000000000000
χ782-2-2-2-22220-2200-202−22−222−22−22-22-2-22-22000000000-222-2-222-20−222−20000−22−222−22−2000000002−2−222−2−220000000000000000
χ792-2-2-2-22220-2200-202−22−222−22−2-22-222-22-20000000002-2-22-222-20−222−200002−22−2−22−2200000000−222−22−2−220000000000000000
χ802-2-2-2-22220-2200-202−22−222−22−2-22-222-22-2000000000-222-22-2-220−222−200002−22−2−22−22000000002−2−22−222−20000000000000000
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χ934-4-444-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i222−22−2222−222222−22000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ944-4-444-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i2−222222−2222−22−222200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ954-4-444-44-400000000−2i22i22i2−2i22i2−2i2−2i22i222−22−2222−222222−2200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ964-4-444-44-400000000−2i22i22i2−2i22i2−2i2−2i22i2−222222−2222−22−2222000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ974-4-4-4-444404-40040-422−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ984-4-4-4-444404-40040-4−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000

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