Finite Group Databasebeta

← Group #102136

Character table — Group #102136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444444444444444444444448888888888888888888888888888888888888888888888882222444488888888
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000002222-2-2-2-22222-2-2-2-20000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000-2-2-2-22222-2-2-2-222220000000000000000
χ192222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
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χ392222-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000002i2i−2i−2i-2-22200000000-2-22200002i2i−2i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
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χ4622-2-222-2-22i2i−2i−2i−2i−2i2i2i000022-2-20000000000002i2i−2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
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χ5422-2-222-2-2−2i−2i2i2i2i2i−2i−2i000022-2-2000000000000−2i−2i2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ31+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
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χ5622-2-222-2-2−2i−2i2i2i2i2i−2i−2i000022-2-2000000000000−2i−2i2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ3−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ5722-2-222-2-2−2i−2i2i2i2i2i−2i−2i0000-2-2220000000000002i2i−2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i22ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ30000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000000000
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χ5922-2-222-2-2−2i−2i2i2i2i2i−2i−2i0000-2-2220000000000002i2i−2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i22ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ300001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0000000000000000
χ6022-2-222-2-2−2i−2i2i2i2i2i−2i−2i0000-2-2220000000000002i2i−2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ30000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000000000
χ6122-2-2-2-2222222-2-2-2-222-2-200000000000022-2-200002−2−222−2−222−2−222−2−22i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ6222-2-2-2-2222222-2-2-2-222-2-200000000000022-2-200002−2−222−2−222−2−222−2−22−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200002i−2i−2i2i0000−2i2i2i−2i0000000000000000
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χ6422-2-2-2-2222222-2-2-2-222-2-200000000000022-2-20000−222−2−222−2−222−2−222−2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000−2i2i2i−2i00002i−2i−2i2i0000000000000000
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χ6922-2-2-2-222-2-2-2-2222222-2-2000000000000-2-22200002−2−222−2−22−222−2−222−22−2−222−2−22−222−2−222−20000-222-20000-222-20000000000000000
χ7022-2-2-2-222-2-2-2-2222222-2-2000000000000-2-22200002−2−222−2−22−222−2−222−2−222−2−222−22−2−222−2−2200002-2-2200002-2-220000000000000000
χ7122-2-2-2-222-2-2-2-2222222-2-2000000000000-2-2220000−222−2−222−22−2−222−2−222−2−222−2−22−222−2−222−200002-2-2200002-2-220000000000000000
χ7222-2-2-2-222-2-2-2-2222222-2-2000000000000-2-2220000−222−2−222−22−2−222−2−22−222−2−222−22−2−222−2−220000-222-20000-222-20000000000000000
χ7322-2-2-2-222-2-2-2-22222-2-22200000000000022-2-200002−2−22−222−2−222−22−2−222−2−22−222−2−222−22−2−22-222-20000-222-200000000000000000000
χ7422-2-2-2-222-2-2-2-22222-2-22200000000000022-2-200002−2−22−222−2−222−22−2−22−222−22−2−222−2−22−222−22-2-2200002-2-2200000000000000000000
χ7522-2-2-2-222-2-2-2-22222-2-22200000000000022-2-20000−222−22−2−222−2−22−222−22−2−22−222−2−222−22−2−222-2-2200002-2-2200000000000000000000
χ7622-2-2-2-222-2-2-2-22222-2-22200000000000022-2-20000−222−22−2−222−2−22−222−2−222−22−2−222−2−22−222−2-222-20000-222-200000000000000000000
χ772-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000002-2002i−2i00000000
χ782-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000-2200−2i2i00000000
χ792-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22-2-22-22−2i2i−2i2i-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ802-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22-2-22-22−2i2i−2i2i-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ812-22-22-22-22i−2i2i−2i2i−2i2i−2i-22-222-22-2−2i2i−2i2i-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ822-22-22-22-22i−2i2i−2i2i−2i2i−2i-22-222-22-2−2i2i−2i2i-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ832-22-22-22-22i−2i2i−2i2i−2i2i−2i-22-22-22-222i−2i2i−2i2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002-2002i−2i0000000000
χ842-22-22-22-22i−2i2i−2i2i−2i2i−2i-22-22-22-222i−2i2i−2i2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000-2200−2i2i0000000000
χ852-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000002-200−2i2i00000000
χ862-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000-22002i−2i00000000
χ872-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-2-22-222i−2i2i−2i-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ882-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-2-22-222i−2i2i−2i-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ892-22-22-22-2−2i2i−2i2i−2i2i−2i2i-22-222-22-22i−2i2i−2i-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ902-22-22-22-2−2i2i−2i2i−2i2i−2i2i-22-222-22-22i−2i2i−2i-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ912-22-22-22-2−2i2i−2i2i−2i2i−2i2i-22-22-22-22−2i2i−2i2i2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002-200−2i2i0000000000
χ922-22-22-22-2−2i2i−2i2i−2i2i−2i2i-22-22-22-22−2i2i−2i2i2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000-22002i−2i0000000000
χ934-44-4-44-444-4-444-4-44000000004-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ944-44-4-44-444-4-444-4-4400000000-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ954-44-4-44-44-444-4-444-4000000004-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ964-44-4-44-44-444-4-444-400000000-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4-444-4-444-4-44-444-400004-4-440000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ984-4-444-4-444-4-44-444-40000-444-4000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ994-4-444-4-44-444-44-4-4400004-4-44000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44-444-44-4-440000-444-40000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-44i−4i4i−4i−4i4i−4i4i4-4-440000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-44-444-44i−4i4i−4i−4i4i−4i4i-444-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-4−4i4i−4i4i4i−4i4i−4i4-4-44000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-4−4i4i−4i4i4i−4i4i−4i-444-40000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

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