Finite Group Databasebeta

← Group #379513

Character table — Group #379513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444222222444444888888884444444488888888888888888888224444444444444488888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ171-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i1-1ii−i−i1-111-1-1ii−i−iii−i−i11-1-111-1-11-1i−ii−i1-1
χ181-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i-11−i−iii-1111-1-1ii−i−i−i−iii11-1-1-1-111-11−ii−ii-11
χ191-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i1-1ii−i−i1-1-1-111−i−iii−i−iii-1-111-1-111-11−iii−i1-1
χ201-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i-11−i−iii-11-1-111−i−iiiii−i−i-1-11111-1-11-1i−i−ii-11
χ211-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i1-1ii−i−i1-111-1-1−i−iiiii−i−i-1-11111-1-1-11−ii−ii-11
χ221-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i-11−i−iii-1111-1-1−i−iii−i−iii-1-111-1-1111-1i−ii−i1-1
χ231-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−i1-1ii−i−i1-1-1-111ii−i−i−i−iii11-1-1-1-1111-1i−i−ii-11
χ241-1-11-1-1111-111-1-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−i-11−i−iii-11-1-111ii−i−iii−i−i11-1-111-1-1-11−iii−i1-1
χ251-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii1-1−i−iii1-1-1-111−i−iiiii−i−i11-1-1-1-1111-1−iii−i-11
χ261-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii-11ii−i−i-11-1-111−i−iii−i−iii11-1-111-1-1-11i−i−ii1-1
χ271-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii1-1−i−iii1-111-1-1ii−i−i−i−iii-1-11111-1-1-11i−ii−i-11
χ281-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-11ii−i−i-1111-1-1ii−i−iii−i−i-1-111-1-1111-1−ii−ii1-1
χ291-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iii1-1−i−iii1-1-1-111ii−i−iii−i−i-1-111-1-111-11i−i−ii1-1
χ301-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iii-11ii−i−i-11-1-111ii−i−i−i−iii-1-11111-1-11-1−iii−i-11
χ311-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii1-1−i−iii1-111-1-1−i−iii−i−iii11-1-111-1-11-1−ii−ii1-1
χ321-1-11-1-1111-111-1-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii-11ii−i−i-1111-1-1−i−iiiii−i−i11-1-1-1-111-11i−ii−i-11
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χ372222-2-2-2-2222222-2-2-2-2-2-200000000000000002i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000002-22-200000000000000000000
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χ402222-2-2-2-2222222-2-2-2-2-2-20000000000000000−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000002-22-200000000000000000000
χ412222-2-2-2-222-2-2-2-2222-22-222-2-222-2-20000000000000000000000002-22-2222-22-2-2-20000000000000000000000000000
χ422222-2-2-2-222-2-2-2-2222-22-222-2-222-2-20000000000000000000000002-22-2-2-2-22-22220000000000000000000000000000
χ432222-2-2-2-222-2-2-2-2222-22-2-2-222-2-222000000000000000000000000-22-2222-22-22-2-20000000000000000000000000000
χ442222-2-2-2-222-2-2-2-2222-22-2-2-222-2-222000000000000000000000000-22-22-2-22-22-2220000000000000000000000000000
χ452222-2-2-2-2-2-22-2-22-2222-220000000022-2-222-2-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002i−2i2i−2i000000000000
χ462222-2-2-2-2-2-22-2-22-2222-220000000022-2-222-2-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000−2i2i−2i2i000000000000
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χ482222-2-2-2-2-2-22-2-22-2222-2200000000-2-222-2-222−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002i−2i2i−2i000000000000
χ492222-2-2-2-2-2-2-222-22-2-222222-2-222-2-2000000000000000000000000-22-2200000000000000002i−2i2i−2i00002i−2i2i−2i00000000
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χ562-2-2222-2-22-222-2-2-2-22-2220000000000000000-22-222-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000000000000000
χ572-2-2222-2-22-2-2-22222-2-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000002i−2i−2i2i2-22i−2i−2i2i-220000000000000000000000000000
χ582-2-2222-2-22-2-2-22222-2-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000002i−2i−2i2i-22−2i2i2i−2i2-20000000000000000000000000000
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χ622-2-2222-2-2-222-22-2-22-222-2000000002i2i−2i−2i−2i−2i2i2i-222-22-2-22000000000000000000000000000000002i−2i−2i2i000000000000
χ632-2-2222-2-2-222-22-2-22-222-200000000−2i−2i2i2i2i2i−2i−2i2-2-22-222-2000000000000000000000000000000002i−2i−2i2i000000000000
χ642-2-2222-2-2-222-22-2-22-222-200000000−2i−2i2i2i2i2i−2i−2i-222-22-2-2200000000000000000000000000000000−2i2i2i−2i000000000000
χ652-2-2222-2-2-22-22-222-222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i00000000000000002-2-220000−2i2i2i−2i00000000
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χ692-2-22-2-222-222-22-22-22-2-222i2i2i2i−2i−2i−2i−2i000000002i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i000000002-2-22000000000000000000000000
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χ722-2-22-2-222-222-22-22-22-2-22−2i−2i−2i−2i2i2i2i2i00000000−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i000000002-2-22000000000000000000000000
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χ7744-4-44i−4i4i−4i000000000000−2i22i2−2222−2i22i2−22222-22i−2i2-22i−2i00000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000000000000000
χ7844-4-44i−4i4i−4i000000000000−2i22i2−2222−2i22i2−2222-22−2i2i-22−2i2i000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i0000000000002i2−2i2−22222i2−2i2−22222-2−2i2i2-2−2i2i000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i0000000000002i2−2i2−22222i2−2i2−2222-222i−2i-222i−2i00000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000000000000000
χ8144-4-4−4i4i−4i4i000000000000−2i22i222−22−2i22i222−222-2−2i2i2-2−2i2i00000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000000000000000
χ8244-4-4−4i4i−4i4i000000000000−2i22i222−22−2i22i222−22-222i−2i-222i−2i000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000000000000000
χ834-44-44i−4i−4i4i00000000000022−222i2−2i2−2222−2i22i22i−2i2-2−2i2i-2200000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000000000000000
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χ854-44-44i−4i−4i4i000000000000−2222−2i22i222−222i2−2i22i−2i2-2−2i2i-22000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000000000000000
χ864-44-44i−4i−4i4i000000000000−2222−2i22i222−222i2−2i2−2i2i-222i−2i2-200000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000000000000000
χ874-44-4−4i4i4i−4i00000000000022−22−2i22i2−22222i2−2i22i−2i-22−2i2i2-200000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000000000000000
χ884-44-4−4i4i4i−4i00000000000022−22−2i22i2−22222i2−2i2−2i2i2-22i−2i-22000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000000000000000
χ894-44-4−4i4i4i−4i000000000000−22222i2−2i222−22−2i22i22i−2i-22−2i2i2-2000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000000000000000
χ904-44-4−4i4i4i−4i000000000000−22222i2−2i222−22−2i22i2−2i2i2-22i−2i-2200000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000000000000000
χ914-4-44-4-4444-4-4-444-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-44-44-44-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000

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