Finite Group Databasebeta

← Group #72313424

Character table — Group #72313424

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size1111222222444444444444444444448888888888888888888888888888161616161616161616161616161616161616161616161616161616163232323232323232
order1222224444222222444444888888884444444488881616161616161616161616161616161622224444444444448888161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−iii−i−iii−i−i
χ10111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111-1-111-1-11111-1-1iiii−i−i−i−i−i−iii−i−iii
χ11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−iii−i−iii
χ12111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111-1-111-1-11111-1-1−i−i−i−iiiiiii−i−iii−i−i
χ13111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiii−i−i−i−iii
χ14111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−iiiii−i−i
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−iiiii−i−i
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-1-11111-1-1-1-111iiii−i−i−i−iii−i−i−i−iii
χ1711-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-11-11-1i−ii−i1-11-1i−ii−ii−ii−iii−i−iii−i−i1-11-1i−ii−i
χ1811-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1-11-11−ii−ii-11-11−ii−iii−ii−iii−i−iii−i−i-11-11−ii−ii
χ1911-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11ii−i−iii−i−i11-1-1-1-1-1-11111-1-1-1-111111-11-1i−ii−i1-11-1i−ii−ii−ii−i−i−iii−i−iii-11-11−ii−ii
χ2011-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11ii−i−iii−i−i11-1-1-1-1-1-11111-1-1-1-11111-11-11−ii−ii-11-11−ii−iii−ii−i−i−iii−i−iii1-11-1i−ii−i
χ2111-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-11-11-1−ii−ii1-11-1−ii−ii−ii−ii−i−iii−i−iii1-11-1−ii−ii
χ2211-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1-11-11i−ii−i-11-11i−ii−i−ii−ii−i−iii−i−iii-11-11i−ii−i
χ2311-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11−i−iii−i−iii11-1-1-1-1-1-11111-1-1-1-111111-11-1−ii−ii1-11-1−ii−ii−ii−iiii−i−iii−i−i-11-11i−ii−i
χ2411-1-11-11-1-111-111-1-11-11-11-1111-1-1-1-11−i−iii−i−iii11-1-1-1-1-1-11111-1-1-1-11111-11-11i−ii−i-11-11i−ii−i−ii−iiii−i−iii−i−i1-11-1−ii−ii
χ2511-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−iii−i−ii-1-11111-1-1i−i−ii-111-1
χ2611-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-111-1−iii−ii−i−ii-1-11111-1-1−iii−i1-1-11
χ2711-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1ii−i−i−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii1-1-11i−i−iii−i−ii11-1-1-1-111−iii−i1-1-11
χ2811-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1ii−i−i−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i-111-1−iii−ii−i−ii11-1-1-1-111i−i−ii-111-1
χ2911-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1−i−iiiii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i1-1-11−iii−i−iii−i11-1-1-1-111i−i−ii1-1-11
χ3011-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1−i−iiiii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii-111-1i−i−ii−iii−i11-1-1-1-111−iii−i-111-1
χ3111-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i−iii−i-1-11111-1-1−iii−i-111-1
χ3211-1-11-11-1-111-1-1-1111-1-11-11-1-1-11111-1−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii−iii−i-1-11111-1-1i−i−ii1-1-11
χ332222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-2-2-20000000000000000
χ342222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022220000000000000000
χ35222222222222-2-2-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2220000000000000000
χ36222222222222-2-2-2-222-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000000022-2-20000000000000000
χ372222222222-2-22-22-2-2-22-2-2222-2-2-222-2000000002-22-2000000000000000022-2-20000-2-222000000000000000000000000
χ382222222222-2-22-22-2-2-22-2-2222-2-2-222-2000000002-22-20000000000000000-2-222000022-2-2000000000000000000000000
χ392222222222-2-22-22-2-2-22-2-22-2-2222-2-2200000000-22-220000000000000000000022220000-2-2-2-200000000000000000000
χ402222222222-2-22-22-2-2-22-2-22-2-2222-2-2200000000-22-2200000000000000000000-2-2-2-20000222200000000000000000000
χ412222222222-2-2-22-22-2-2-222-222-2-2-222-200000000-22-220000000000000000000022-2-20000-2-22200000000000000000000
χ422222222222-2-2-22-22-2-2-222-222-2-2-222-200000000-22-2200000000000000000000-2-222000022-2-200000000000000000000
χ432222222222-2-2-22-22-2-2-222-2-2-2222-2-22000000002-22-2000000000000000022220000-2-2-2-2000000000000000000000000
χ442222222222-2-2-22-22-2-2-222-2-2-2222-2-22000000002-22-20000000000000000-2-2-2-200002222000000000000000000000000
χ45222222-2-2-2-2-2-2222222-2-2-2-2000000002-22-22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ46222222-2-2-2-2-2-2222222-2-2-2-2000000002-22-22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ47222222-2-2-2-2-2-2222222-2-2-2-200000000-22-22-22-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ48222222-2-2-2-2-2-2222222-2-2-2-200000000-22-22-22-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ49222222-2-2-2-2-2-2-2-2-2-2222222000000002-22-2-22-22000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ50222222-2-2-2-2-2-2-2-2-2-2222222000000002-22-2-22-220000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ51222222-2-2-2-2-2-2-2-2-2-222222200000000-22-222-22-2000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ52222222-2-2-2-2-2-2-2-2-2-222222200000000-22-222-22-20000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ5322-2-22-22-2-222-222-2-22-22-22-2-2-2-22222-22i2i−2i−2i2i2i−2i−2i-2-22200000000000000000000000000000000−2i2i−2i2i0000000000000000
χ5422-2-22-22-2-222-222-2-22-22-22-2-2-2-22222-2−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000000000000000002i−2i2i−2i0000000000000000
χ5522-2-22-22-2-222-2-2-2222-2-22-22222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-22200000000000000000000000000000000−2i2i2i−2i0000000000000000
χ5622-2-22-22-2-222-2-2-2222-2-22-22222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000002i−2i−2i2i0000000000000000
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χ6022-2-22-22-2-22-222-2-22-2222-2-2-2-22-2-222200000000-222-200000000000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ6122-2-22-22-2-22-22-222-2-22-2-22222-222-2-2-200000000-222-2000000000000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
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χ6422-2-22-22-2-22-22-222-2-22-2-222-2-22-2-2222000000002-2-220000000000000000-22-2200002-22-2000000000000000000000000
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χ784444-4-444-4-4000000000000−4i4i000−4i4i0000000000000−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000000000000000
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χ8644-4-4-444-44-40000000000004i−4i000−4i4i0000000000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000000000
χ8744-4-4-444-44-4000000000000−4i4i0004i−4i00000000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000000000000000
χ8844-4-4-444-44-4000000000000−4i4i0004i−4i0000000000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000000000000000
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χ9144-4-4-44-44-4400000000000000-44-40040000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ9244-4-4-44-44-4400000000000000-44-4004000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ9316-1616-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9416-16-1616000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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