Finite Group Databasebeta

← Group #161491

Character table — Group #161491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444444444444444444444444224444444444888888888888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-111-1-1−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-111-1-111iiii−i−i−i−i
χ9111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ11111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−iii
χ12111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1711111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ1911111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ2011111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ2111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-111-11-1-11-11
χ2211111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-11-111-11-1
χ2311111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-111-1-11-11-111-11-1
χ2411111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-111-11-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-11-111-1-111-1-11
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-111-11-1-111-1-111-1
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1-11-11-111-1-111-1
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-111-11-11-1-111-1-11
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1i−i−ii−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11−iii−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1−iii−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-11-1-11i−i−ii−iii−i
χ3322222222222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22222-2-222000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222222222222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-222-2-2222222-2-2-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-22222-2-2222222-2-2-2-222000000000000000000000000000000000000000000000000
χ41222-22-2-2-222-2-222-2-222-2-2000022-2-222000000000000-2-22-2002-200000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ42222-22-2-2-222-2-222-2-222-2-2000022-2-222000000000000-2-22-2002-2000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
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χ44222-22-2-2-222-2-222-2-2-2-2220000-2-222-2-2000000000000222-200-22000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ45222-22-2-2-222-2-2-2-22222-2-20000-2-222-2-200000000000022-22002-2000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ46222-22-2-2-222-2-2-2-22222-2-20000-2-222-2-200000000000022-22002-2000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ47222-22-2-2-222-2-2-2-222-2-222000022-2-222000000000000-2-2-2200-2200000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ48222-22-2-2-222-2-2-2-222-2-222000022-2-222000000000000-2-2-2200-22000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ49222-22-2-2-2-2-22222-2-222-2-2000022-2-2-2-200000000000022-2200-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ50222-22-2-2-2-2-22222-2-222-2-2000022-2-2-2-200000000000022-2200-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ51222-22-2-2-2-2-22222-2-2-2-2220000-2-22222000000000000-2-2-22002-200000022−2−2−2−22222−2−2−2−222−2−22222−2−2−2−22222−2−20000000000000000
χ52222-22-2-2-2-2-22222-2-2-2-2220000-2-22222000000000000-2-2-22002-2000000−2−22222−2−2−2−22222−2−222−2−2−2−22222−2−2−2−2220000000000000000
χ53222-22-2-2-2-2-222-2-22222-2-20000-2-22222000000000000-2-22-200-2200000022−2−2−2−222−2−22222−2−222−2−2−2−222−2−22222−2−20000000000000000
χ54222-22-2-2-2-2-222-2-22222-2-20000-2-22222000000000000-2-22-200-22000000−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2−2−2220000000000000000
χ55222-22-2-2-2-2-222-2-222-2-222000022-2-2-2-2000000000000222-2002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
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χ5922-22-2-2-222-22-20000000000002i−2i2i−2i2i−2i-2-2220000−2i−2i2i2i2i−2i000000−2i2i-22002ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ300000000000000002ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ0000000000000000
χ6022-22-2-2-222-22-20000000000002i−2i2i−2i2i−2i-2-2220000−2i−2i2i2i2i−2i000000−2i2i-2200−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ30000000000000000−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ0000000000000000
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χ6222-22-2-2-222-22-2000000000000−2i2i−2i2i−2i2i22-2-20000−2i−2i2i2i−2i2i000000−2i2i2-20000000000−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000
χ6322-22-2-2-222-22-2000000000000−2i2i−2i2i−2i2i-2-22200002i2i−2i−2i−2i2i0000002i−2i-22002ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ00000000000000002ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ30000000000000000
χ6422-22-2-2-222-22-2000000000000−2i2i−2i2i−2i2i-2-22200002i2i−2i−2i−2i2i0000002i−2i-2200−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ30000000000000000
χ6522-22-2-2-22-22-220000000000002i−2i2i−2i−2i2i22-2-200002i2i−2i−2i−2i2i000000−2i2i-22002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ0000000000000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ30000000000000000
χ6622-22-2-2-22-22-220000000000002i−2i2i−2i−2i2i22-2-200002i2i−2i−2i−2i2i000000−2i2i-2200−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ00000000000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ30000000000000000
χ6722-22-2-2-22-22-220000000000002i−2i2i−2i−2i2i-2-2220000−2i−2i2i2i−2i2i0000002i−2i2-200000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000
χ6822-22-2-2-22-22-220000000000002i−2i2i−2i−2i2i-2-2220000−2i−2i2i2i−2i2i0000002i−2i2-20000000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000
χ6922-22-2-2-22-22-22000000000000−2i2i−2i2i2i−2i22-2-20000−2i−2i2i2i2i−2i0000002i−2i-22002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ30000000000000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ0000000000000000
χ7022-22-2-2-22-22-22000000000000−2i2i−2i2i2i−2i22-2-20000−2i−2i2i2i2i−2i0000002i−2i-2200−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ300000000000000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ0000000000000000
χ7122-22-2-2-22-22-22000000000000−2i2i−2i2i2i−2i-2-22200002i2i−2i−2i2i−2i000000−2i2i2-200000000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ7222-22-2-2-22-22-22000000000000−2i2i−2i2i2i−2i-2-22200002i2i−2i−2i2i−2i000000−2i2i2-20000000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.