Finite Group Databasebeta

← Group #98910

Character table — Group #98910

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444444444444444888888888888888888888888888888882444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ9111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ10111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii−i−iii-1-111
χ11111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ12111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111
χ13111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii-1-111
χ14111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i11-1-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i-1-111
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii11-1-1
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χ182222222222222222-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i
χ2122222222-2-2-2-2222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ2222222222-2-2-2-2222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-22-2000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-22-22000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222222-2-222-2-2000000000000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222222-2-222-2-200000000000000000000000000000000-222-2000000000000
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χ31222-2-22-2-200002i2i−2i−2i2-200002i2i−2i−2i2-20000-2-222−2i−2i2i2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ32222-2-22-2-200002i2i−2i−2i2-200002i2i−2i−2i2-20000-2-222−2i−2i2i2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
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χ34222-2-22-2-20000−2i−2i2i2i2-20000−2i−2i2i2i2-2000022-2-2−2i−2i2i2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
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χ392-2-2222-2-222-2-22i−2i2i−2i-222i2i−2i−2i−2i2i−2i2i2-2-22−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ402-2-2222-2-222-2-22i−2i2i−2i-222i2i−2i−2i−2i2i−2i2i2-2-22−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ412-2-2222-2-222-2-2−2i2i−2i2i2-2−2i−2i2i2i−2i2i−2i2i-222-2−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ422-2-2222-2-222-2-2−2i2i−2i2i2-2−2i−2i2i2i−2i2i−2i2i-222-2−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ432-2-2222-2-222-2-2−2i2i−2i2i-22−2i−2i2i2i2i−2i2i−2i2-2-222i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ442-2-2222-2-222-2-2−2i2i−2i2i-22−2i−2i2i2i2i−2i2i−2i2-2-222i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ452-2-2222-2-2-2-2222i−2i2i−2i2-2−2i−2i2i2i2i−2i2i−2i-22-22−2i2i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ462-2-2222-2-2-2-2222i−2i2i−2i2-2−2i−2i2i2i2i−2i2i−2i-22-22−2i2i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ472-2-2222-2-2-2-2222i−2i2i−2i-22−2i−2i2i2i−2i2i−2i2i2-22-22i−2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ482-2-2222-2-2-2-2222i−2i2i−2i-22−2i−2i2i2i−2i2i−2i2i2-22-22i−2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ492-2-2222-2-2-2-222−2i2i−2i2i2-22i2i−2i−2i−2i2i−2i2i-22-222i−2i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ502-2-2222-2-2-2-222−2i2i−2i2i2-22i2i−2i−2i−2i2i−2i2i-22-222i−2i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ512-2-2222-2-2-2-222−2i2i−2i2i-222i2i−2i−2i2i−2i2i−2i2-22-2−2i2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ522-2-2222-2-2-2-222−2i2i−2i2i-222i2i−2i−2i2i−2i2i−2i2-22-2−2i2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ532-2-2-2-222200002-2-222200002-2-22-2-20000000000002i2i−2i−2i2i2i−2i−2ii2−i2−i2i2i2−i2−i2i22−2−22−222−20000000000000000
χ542-2-2-2-222200002-2-222200002-2-22-2-20000000000002i2i−2i−2i2i2i−2i−2i−i2i2i2−i2−i2i2i2−i2−222−22−2−220000000000000000
χ552-2-2-2-222200002-2-222200002-2-22-2-2000000000000−2i−2i2i2i−2i−2i2i2ii2−i2−i2i2i2−i2−i2i2−222−22−2−220000000000000000
χ562-2-2-2-222200002-2-222200002-2-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i−i2i2i2−i2−i2i2i2−i22−2−22−222−20000000000000000
χ572-2-2-2-22220000-222-2220000-222-2-2-20000000000002i2i−2i−2i−2i−2i2i2i2−2−22−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ582-2-2-2-22220000-222-2220000-222-2-2-20000000000002i2i−2i−2i−2i−2i2i2i−222−22−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ592-2-2-2-22220000-222-2220000-222-2-2-2000000000000−2i−2i2i2i2i2i−2i−2i2−2−22−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ602-2-2-2-22220000-222-2220000-222-2-2-2000000000000−2i−2i2i2i2i2i−2i−2i−222−22−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ61444-4-44-4-400004i4i−4i−4i-440000−4i−4i4i4i-440000000000000000000000000000000000000000000000000000
χ62444-4-44-4-40000−4i−4i4i4i-4400004i4i−4i−4i-440000000000000000000000000000000000000000000000000000
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χ6544-44-4-44-40000000000-44-44000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
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χ6744-4-44-4-444i−4i4i−4i00000000000000000000000022−22−222200002i2−2i22i2−2i200000000000000000000000000000000
χ6844-4-44-4-444i−4i4i−4i000000000000000000000000−222222−220000−2i22i2−2i22i200000000000000000000000000000000
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χ7044-4-44-4-44−4i4i−4i4i000000000000000000000000−222222−2200002i2−2i22i2−2i200000000000000000000000000000000
χ714-444-4-4-4400000000004i−4i−4i4i00000000002i2−2i22i2−2i20000000022−22−222200000000000000000000000000000000
χ724-444-4-4-4400000000004i−4i−4i4i0000000000−2i22i2−2i22i200000000−222222−2200000000000000000000000000000000
χ734-444-4-4-440000000000−4i4i4i−4i00000000002i2−2i22i2−2i200000000−222222−2200000000000000000000000000000000
χ744-444-4-4-440000000000−4i4i4i−4i0000000000−2i22i2−2i22i20000000022−22−222200000000000000000000000000000000
χ754-44-44-44-44i−4i−4i4i000000000000000000002i2−2i2−2i22i2000022−22−2222000000000000000000000000000000000000
χ764-44-44-44-44i−4i−4i4i00000000000000000000−2i22i22i2−2i20000−222222−22000000000000000000000000000000000000
χ774-44-44-44-4−4i4i4i−4i000000000000000000002i2−2i2−2i22i20000−222222−22000000000000000000000000000000000000
χ784-44-44-44-4−4i4i4i−4i00000000000000000000−2i22i22i2−2i2000022−22−2222000000000000000000000000000000000000
χ794-4-4-4-444400004-4-44-4-40000-444-4440000000000000000000000000000000000000000000000000000
χ804-4-4-4-44440000-444-4-4-400004-4-44440000000000000000000000000000000000000000000000000000

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