Finite Group Databasebeta

← Group #161502

Character table — Group #161502

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222222222444444444444444444444444444444444444888888888888888888888888888888882244444488888888
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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-111-1-11-1iiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-11-1-111-11−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1-111-1-11-1−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-11-1-111-11iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111-111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-11-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1-1111-1-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-111
χ1711111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i111-11-1-1-1i−ii−ii−ii−i
χ1811111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-11-1111−ii−ii−ii−ii
χ1911111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii111-11-1-1-1−ii−ii−ii−ii
χ2011111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-1-11-1111i−ii−ii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-111-11-1-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-11-1-11-111-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-1-11-11-11-111-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-111-11-11-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-11-11-1-11-1-111-1-11
χ2611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-11-111-111-1-111-1
χ2711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11-1-1-111-1-111-1
χ2811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-11-1111-1-111-1-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11i−i−ii−iii−i
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1−iii−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11−iii−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-111-1i−i−ii−iii−i
χ332222222222222222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
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χ35222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-22222000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2222222-2-2-2-22222000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-222222222-2-222-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000000000
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χ45222-2-2-2-2222-2-20000000000000000−2i−2i2i2i−2i2i22-2-2−2i−2i2i2i−2i2i0000−2i2i2-20000000000002ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000
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χ47222-2-2-2-2222-2-20000000000000000−2i−2i2i2i−2i2i-2-2222i2i−2i−2i−2i2i00002i−2i-2200002ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ300000000000000002ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ0000000000000000
χ48222-2-2-2-2222-2-20000000000000000−2i−2i2i2i−2i2i-2-2222i2i−2i−2i−2i2i00002i−2i-220000−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ30000000000000000−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ0000000000000000
χ49222-2-2-2-22-2-22200000000000000002i2i−2i−2i−2i2i22-2-22i2i−2i−2i−2i2i0000−2i2i-2200002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ30000000000000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ0000000000000000
χ50222-2-2-2-22-2-22200000000000000002i2i−2i−2i−2i2i22-2-22i2i−2i−2i−2i2i0000−2i2i-220000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ300000000000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ0000000000000000
χ51222-2-2-2-22-2-22200000000000000002i2i−2i−2i−2i2i-2-222−2i−2i2i2i−2i2i00002i−2i2-20000000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000
χ52222-2-2-2-22-2-22200000000000000002i2i−2i−2i−2i2i-2-222−2i−2i2i2i−2i2i00002i−2i2-2000000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000
χ53222-2-2-2-22-2-2220000000000000000−2i−2i2i2i2i−2i22-2-2−2i−2i2i2i2i−2i00002i−2i-2200002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ0000000000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ30000000000000000
χ54222-2-2-2-22-2-2220000000000000000−2i−2i2i2i2i−2i22-2-2−2i−2i2i2i2i−2i00002i−2i-220000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ00000000000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ30000000000000000
χ55222-2-2-2-22-2-2220000000000000000−2i−2i2i2i2i−2i-2-2222i2i−2i−2i2i−2i0000−2i2i2-20000000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ56222-2-2-2-22-2-2220000000000000000−2i−2i2i2i2i−2i-2-2222i2i−2i−2i2i−2i0000−2i2i2-2000000000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ5722-222-2-2-20000000022-2-200002i2i−2i−2i2i−2i2i−2i002i−2i2i−2i2-22-2002-20000002i−2i00i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−2i2−i2i2−i20000000000000000
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χ6522-222-2-2-200000000-2-22200002i2i−2i−2i−2i2i−2i2i002i−2i2i−2i-22-22002-2000000−2i2i002−22−2−i2i2−i2i2i2−i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i2−22−220000000000000000
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χ6722-222-2-2-200000000-2-22200002i2i−2i−2i−2i2i−2i2i00−2i2i−2i2i2-22-200-220000002i−2i00i2−i2i2−i2−22−222−22−2−i2i2−i2i2−i2i2−i2i22−22−2−22−22i2−i2i2−i20000000000000000
χ6822-222-2-2-200000000-2-22200002i2i−2i−2i−2i2i−2i2i00−2i2i−2i2i2-22-200-220000002i−2i00−i2i2−i2i22−22−2−22−22i2−i2i2−i2i2−i2i2−i2−22−222−22−2−i2i2−i2i20000000000000000
χ6922-222-2-2-200000000-2-2220000−2i−2i2i2i2i−2i2i−2i002i−2i2i−2i2-22-200-22000000−2i2i00i2−i2i2−i22−22−2−22−22−i2i2−i2i2−i2i2−i2i2−22−222−22−2i2−i2i2−i20000000000000000
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χ994-4-44-4-444-44-444-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1014-4-4-444-444-4-44000000004-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-444-444-4-4400000000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-444-44-444-4000000004-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-44-444-400000000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.