Finite Group Databasebeta

← Group #136607

Character table — Group #136607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444224444444444888888882244444488881616161616161616161616161616161688888888888888888888161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111
χ91111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i11-1-111-1-1
χ101111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii−i−i−i−iiiii11-1-1iiii−i−i−i−i-1-111-1-111
χ111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−iiiii−i−i−i−i11-1-1−i−i−i−iiiii-1-111-1-111
χ121111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii−i−i−i−iiiii11-1-1−i−i−i−iiiii11-1-111-1-1
χ131111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-1-11111-1-1
χ141111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iiiiiii−i−i−i−i-1-111−i−i−i−iiiii11-1-1-1-111
χ151111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i−i−i−i−iiiii-1-111iiii−i−i−i−i11-1-1-1-111
χ161111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iiiiiii−i−i−i−i-1-111iiii−i−i−i−i-1-11111-1-1
χ1711-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i1-11-1i−ii−i1-1i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ61-1i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ61-1i−i1-1i−i
χ1811-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i1-11-1i−ii−i1-1i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ61-1i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-11−ii-11−ii
χ1911-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i1-11-1i−ii−i1-1i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ61-1i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-11−ii-11−ii
χ2011-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i1-11-1i−ii−i1-1i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ61-1i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ61-1i−i1-1i−i
χ2111-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i-11-11−ii−ii1-1i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-11−ii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-11−ii1-1i−i
χ2211-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i-11-11−ii−ii1-1i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-11−ii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ61-1i−i-11−ii
χ2311-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i-11-11−ii−ii1-1i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-11−iiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ61-1i−i-11−ii
χ2411-1-1i−ii−i1-1ii−i−ii−i11-1-111-1-1ii−i−i-11-11−ii−ii1-1i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-11−iiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-11−ii1-1i−i
χ2511-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii1-11-1−ii−ii1-1−iiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ21-1−iiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ21-1−ii1-1−ii
χ2611-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii1-11-1−ii−ii1-1−iiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ21-1−iiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-11i−i-11i−i
χ2711-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii1-11-1−ii−ii1-1−ii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ21-1−ii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-11i−i-11i−i
χ2811-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii1-11-1−ii−ii1-1−ii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ21-1−ii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ21-1−ii1-1−ii
χ2911-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii-11-11i−ii−i1-1−iiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-11i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-11i−i1-1−ii
χ3011-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii-11-11i−ii−i1-1−iiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-11i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ21-1−ii-11i−i
χ3111-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii-11-11i−ii−i1-1−ii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-11i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ21-1−ii-11i−i
χ3211-1-1−ii−ii1-1−i−iii−ii11-1-111-1-1−i−iii-11-11i−ii−i1-1−ii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-11i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-11i−i1-1−ii
χ3322222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-2-2-20000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022220000000000000000
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χ3622222222-2-22-22-2-2-22-22-20000000022-2-2-2-2220000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ3722222222-2-22-22-2-2-22-22-200000000-2-22222-2-2000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ3822222222-2-22-22-2-2-22-22-200000000-2-22222-2-20000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
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χ4022222222-2-2-22-22-2-2-22-222222222200000000-2-2-2-20000000000000000-2-2-2-222220000000000000000000000000000
χ4122222222-2-2-22-22-2-2-22-22-2-2-2-2-2-2-2-20000000022220000000000000000000000002-22-22-22-200000000000000000000
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χ432222-2-2-2-222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-22200000000000000000000000000000000-2-2220000000000000000
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χ462222-2-2-2-2-2-22-22-222-22-222222-2-2-2-200000000-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ472222-2-2-2-2-2-22-22-222-22-22-2-2-2-222220000000022-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ482222-2-2-2-2-2-22-22-222-22-22-2-2-2-222220000000022-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ492222-2-2-2-2-2-2-22-22222-22-20000000022-2-222-2-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ502222-2-2-2-2-2-2-22-22222-22-20000000022-2-222-2-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ512222-2-2-2-2-2-2-22-22222-22-200000000-2-222-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ522222-2-2-2-2-2-2-22-22222-22-200000000-2-222-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ5322-2-22i−2i2i−2i2-22i2i−2i−2i2i−2i22-2-2-2-222−2i−2i2i2i2-22-22i−2i2i−2i-22−2i2i00000000000000000000000000000000-22−2i2i0000000000000000
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χ5522-2-22i−2i2i−2i-222i−2i−2i2i−2i2i2-2-22000000002-2-22−2i2i2i−2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
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χ6022-2-22i−2i2i−2i-22−2i2i2i−2i−2i2i-222-222-2-22i2i−2i−2i00000000-22−2i2i0000000000000000−2ζ22ζ2−2ζ62ζ62ζ2−2ζ22ζ6−2ζ60000000000000000000000000000
χ6122-2-22i−2i2i−2i-22−2i2i2i−2i−2i2i-222-2-2-222−2i−2i2i2i000000002-22i−2i0000000000000000000000002ζ2−2ζ2−2ζ22ζ22ζ6−2ζ6−2ζ62ζ600000000000000000000
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χ6322-2-2−2i2i−2i2i2-2−2i−2i2i2i−2i2i22-2-2-2-2222i2i−2i−2i2-22-2−2i2i−2i2i-222i−2i00000000000000000000000000000000-222i−2i0000000000000000
χ6422-2-2−2i2i−2i2i2-2−2i−2i2i2i−2i2i22-2-2-2-2222i2i−2i−2i-22-222i−2i2i−2i-222i−2i000000000000000000000000000000002-2−2i2i0000000000000000
χ6522-2-2−2i2i−2i2i-222i−2i−2i2i2i−2i-222-222-2-2−2i−2i2i2i00000000-222i−2i00000000000000002ζ6−2ζ62ζ2−2ζ2−2ζ62ζ6−2ζ22ζ20000000000000000000000000000
χ6622-2-2−2i2i−2i2i-222i−2i−2i2i2i−2i-222-222-2-2−2i−2i2i2i00000000-222i−2i0000000000000000−2ζ62ζ6−2ζ22ζ22ζ6−2ζ62ζ2−2ζ20000000000000000000000000000
χ6722-2-2−2i2i−2i2i-222i−2i−2i2i2i−2i-222-2-2-2222i2i−2i−2i000000002-2−2i2i0000000000000000000000002ζ6−2ζ6−2ζ62ζ62ζ2−2ζ2−2ζ22ζ200000000000000000000
χ6822-2-2−2i2i−2i2i-222i−2i−2i2i2i−2i-222-2-2-2222i2i−2i−2i000000002-2−2i2i000000000000000000000000−2ζ62ζ62ζ6−2ζ6−2ζ22ζ22ζ2−2ζ200000000000000000000
χ6922-2-2−2i2i−2i2i-22−2i2i2i−2i2i−2i2-2-22000000002-2-222i−2i−2i2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ7022-2-2−2i2i−2i2i-22−2i2i2i−2i2i−2i2-2-22000000002-2-222i−2i−2i2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ7122-2-2−2i2i−2i2i-22−2i2i2i−2i2i−2i2-2-2200000000-222-2−2i2i2i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ7222-2-2−2i2i−2i2i-22−2i2i2i−2i2i−2i2-2-2200000000-222-2−2i2i2i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.