Finite Group Databasebeta

← Group #10695084

Character table — Group #10695084

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12224444223444444444466612121212444444446612121212121212121212121212121212121212121212121212128888888888888888448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ172222222222222-2-2-2-2-2-2-2-2222222222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ192222222222-12222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ212222222222-12222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ222222222222-12222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ232222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ242222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ252222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1111111111111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ262222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1111111111111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2722222222-2-22-2-222-2-2-2-222222222200000000-2-2-2-222-2-222-2-200000000000000000000000022-2-222-2-20000000000000000
χ2822222222-2-22-2-222-2-2-2-222222222200000000-2-2-2-222-2-222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2922222222-2-22-2-2-2-22222-2-2222222200000000-2-2-2-2-2-222-2-222000000000000000022-2-222-2-2000000000000000000000000
χ3022222222-2-22-2-2-2-22222-2-2222222200000000-2-2-2-2-2-222-2-2220000000000000000-2-222-2-222000000000000000000000000
χ312222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-20000000022-2-222-2-2-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-20000000022-2-222-2-2-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-20000000022-2-2-2-22222-2-2000000000000000022-2-2-2-222000000000000000000000000
χ342222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-20000000022-2-2-2-22222-2-20000000000000000-2-22222-2-2000000000000000000000000
χ352222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ362222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-222-2-2-1-1-111112i2i2i2i−2i−2i−2i−2i11-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i-1-111−i−iii0000
χ382222-2-2-2-2-2-2-12222-2-222-2-2-1-1-111112i2i2i2i−2i−2i−2i−2i11-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ392222-2-2-2-2-2-2-12222-2-222-2-2-1-1-11111−2i−2i−2i−2i2i2i2i2i11-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ402222-2-2-2-2-2-2-12222-2-222-2-2-1-1-11111−2i−2i−2i−2i2i2i2i2i11-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ412222-2-2-2-2-2-2-122-2-222-2-222-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−i3i3i3−i33−3−330000
χ422222-2-2-2-2-2-2-122-2-222-2-222-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000i3−i3−i3i3−333−30000
χ432222-2-2-2-2-2-2-122-2-222-2-222-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−i3i3i3−i3−333−30000
χ442222-2-2-2-2-2-2-122-2-222-2-222-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000i3−i3−i3i33−3−330000
χ4522-2-222-2-22-222-2000000002-2-222-2-2002-2002-22-22-200000000000022-2-2000022-2-22−22−22−22−22−22−22−22−20000000000000000
χ4622-2-222-2-22-222-2000000002-2-222-2-2002-2002-22-22-200000000000022-2-2000022-2-2−22−22−22−22−22−22−22−220000000000000000
χ4722-2-222-2-22-222-2000000002-2-222-2-200-2200-222-22-2000000000000-2-2220000-2-2222−22−22−22−2−22−22−22−220000000000000000
χ4822-2-222-2-22-222-2000000002-2-222-2-200-2200-222-22-2000000000000-2-2220000-2-222−22−22−22−222−22−22−22−20000000000000000
χ4922-2-222-2-2-222-22000000002-2-222-2-22-2002-200-22-220000000022-2-2000022-2-200002−2−222−2−222−2−222−2−220000000000000000
χ5022-2-222-2-2-222-22000000002-2-222-2-22-2002-200-22-220000000022-2-2000022-2-20000−222−2−222−2−222−2−222−20000000000000000
χ5122-2-222-2-2-222-22000000002-2-222-2-2-2200-2200-22-2200000000-2-2220000-2-22200002−2−222−2−22−222−2−222−20000000000000000
χ5222-2-222-2-2-222-22000000002-2-222-2-2-2200-2200-22-2200000000-2-2220000-2-2220000−222−2−222−22−2−222−2−220000000000000000
χ5322-2-2-2-2222-22-22000000002-2-2-2-2222i−2i00−2i2i002-2-22000000002i2i−2i−2i0000−2i−2i2i2i00002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5422-2-2-2-2222-22-22000000002-2-2-2-2222i−2i00−2i2i002-2-22000000002i2i−2i−2i0000−2i−2i2i2i0000−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ5522-2-2-2-2222-22-22000000002-2-2-2-222−2i2i002i−2i002-2-2200000000−2i−2i2i2i00002i2i−2i−2i00002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
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χ5722-2-2-2-222-2222-2000000002-2-2-2-222002i−2i00−2i2i-222-20000000000002i2i−2i−2i0000−2i−2i2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ5822-2-2-2-222-2222-2000000002-2-2-2-222002i−2i00−2i2i-222-20000000000002i2i−2i−2i0000−2i−2i2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.