Finite Group Databasebeta

← Group #10714543

Character table — Group #10714543

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order1222222234444666666688888888444488881212121212121212121212122424242424242424242424242424242416161616161616161616161616161616444412121212121212124444
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ922222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ11222222222-2-2-2-222222220000000022-2-20000-2-22222-2-2-2-2-2-200000000000000002222−2−2−2−22222−2−2−2−20000000000000000
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χ13222222222-2-2-2-2222222200000000-2-2220000-2-2-2-2-2-22222-2-200000000000000002222−2−2−2−2−2−2−2−222220000000000000000
χ14222222222-2-2-2-2222222200000000-2-2220000-2-2-2-2-2-22222-2-20000000000000000−2−2−2−222222222−2−2−2−20000000000000000
χ1522222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ1622222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ1722222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ1822222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ1922222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3−i3i3i3−i3−i3i3i30000
χ2022222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3i3−i3−i3i3i3−i3−i30000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3−i3i3i3i3i3−i3−i30000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3i3−i3−i3−i3−i3i3i30000
χ23222-22-2-2-22000022-22-2-2-222−2−222−2−22-20022−2−20022-2-20000002222−2−2−2−22222−2−2−2−2−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ430000000000000000
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χ27222-22-2-2-22000022-22-2-2-2−2−222−2−2222-200−2−2220022-2-2000000−2−2−2−22222−2−2−2−22222ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ470000000000000000
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χ29222-22-2-2-22000022-22-2-2-2−2−222−2−222-220022−2−200-2-222000000−2−2−2−222222222−2−2−2−2ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ470000000000000000
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χ3122-22-2-2-2222-22-22-22-22-2-20000000000002-22-22-2000000002-20000000022-2-222-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-22-2-2-2222-22-22-22-22-2-20000000000002-22-22-2000000002-20000000022-2-222-2-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-22-2-2-2222-22-22-22-22-2-2000000000000-22-222-2000000002-200000000-2-222-2-222−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3422-22-2-2-2222-22-22-22-22-2-2000000000000-22-222-2000000002-200000000-2-222-2-222i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3522-22-2-2-222-22-222-22-22-2-22-22-22-22-200000000-2200000000-2222-2-222-2-200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ3622-22-2-2-222-22-222-22-22-2-22-22-22-22-200000000-2200000000-2222-2-222-2-20000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ3722-22-2-2-222-22-222-22-22-2-2-22-22-22-2200000000-2200000000-22-2-222-2-222000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ3822-22-2-2-222-22-222-22-22-2-2-22-22-22-2200000000-2200000000-22-2-222-2-22200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ3922-2-2-222-2200002-2-2-2-2222−2−222−2−22002-22−2−2200000022-2-20022−2−2−2−22222−2−2−2−222−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000000000
χ4022-2-2-222-2200002-2-2-2-2222−2−222−2−22002-22−2−2200000022-2-20022−2−2−2−22222−2−2−2−222ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000000000
χ4122-2-2-222-2200002-2-2-2-2222−2−222−2−2200-22−222−2000000-2-2220022−2−2−2−222−2−22222−2−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000000000
χ4222-2-2-222-2200002-2-2-2-2222−2−222−2−2200-22−222−2000000-2-2220022−2−2−2−222−2−22222−2−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000000000
χ4322-2-2-222-2200002-2-2-2-222−222−2−222−2002-2−222−200000022-2-200−2−22222−2−2−2−22222−2−2ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000000000000000
χ4422-2-2-222-2200002-2-2-2-222−222−2−222−2002-2−222−200000022-2-200−2−22222−2−2−2−22222−2−2−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000000000000000
χ4522-2-2-222-2200002-2-2-2-222−222−2−222−200-222−2−22000000-2-22200−2−22222−2−222−2−2−2−222ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000000000000000
χ4622-2-2-222-2200002-2-2-2-222−222−2−222−200-222−2−22000000-2-22200−2−22222−2−222−2−2−2−222−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000000000000000
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χ6944-44-4-4-44-24-44-4-22-22-2220000000000004-44-4-2200000000-2200000000-2-222-2-22200000000000000000000000000000000
χ7044-44-4-4-44-24-44-4-22-22-222000000000000-44-44-2200000000-220000000022-2-222-2-200000000000000000000000000000000
χ7144-44-4-4-44-2-44-44-22-22-2224-44-44-44-4000000002-2000000002-2-2-222-2-2220000000000000000000000000000000000000000
χ7244-44-4-4-44-2-44-44-22-22-222-44-44-44-44000000002-2000000002-222-2-222-2-20000000000000000000000000000000000000000
χ7344-4-4-444-4-20000-22222-2-222−22−222222−22−2222004-422−22−2222000000-2-22200−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ7444-4-4-444-4-20000-22222-2-222−22−222222−22−222200-44−222222−2200000022-2-200−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ7544-4-4-444-4-20000-22222-2-2−222222−22−222222−22004-4−222222−22000000-2-2220022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ7644-4-4-444-4-20000-22222-2-2−222222−22−222222−2200-4422−22−222200000022-2-20022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ774-444-4-44-440000-444-4-4-442222−22−22−22−2222220000000000000000000022−2222−22−2222−22220000000000000000000000000000000000000000
χ784-444-4-44-440000-444-4-4-44−22−2222222222−22−2200000000000000000000−2222−222222−2222−220000000000000000000000000000000000000000
χ794-444-4-44-4-200002-2-2222-22222−22−22−22−222222000000000023−23−2323000000−22−222−22−26−66−6−66−6600000000000000000000000000000000
χ804-444-4-44-4-200002-2-2222-22222−22−22−22−2222220000000000−232323−23000000−22−222−22−2−66−666−66−600000000000000000000000000000000
χ814-444-4-44-4-200002-2-2222-2−22−2222222222−22−22000000000023−23−23230000002−22−2−22−22−66−666−66−600000000000000000000000000000000
χ824-444-4-44-4-200002-2-2222-2−22−2222222222−22−220000000000−232323−230000002−22−2−22−226−66−6−66−6600000000000000000000000000000000
χ834-44-4-44-444-444-4-44-4-444-40000000000000000-44000000004-4000000000000000000000000000000000000000000000000
χ844-44-4-44-44-2-444-42-222-2-2200000000000000002-223−2323−23−2323−2323-22000000000000000000000000000000000000000000000000
χ854-44-4-44-44-2-444-42-222-2-2200000000000000002-2−2323−232323−2323−23-22000000000000000000000000000000000000000000000000
χ864-4-4444-4-440000-4-444-44-422−22−2222−222222−220000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ874-4-4444-4-440000-4-444-44-4−222222−2222−22−222200000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ884-4-4444-4-4-2000022-2-22-2222−22−2222−222222−220000000000000023−23−232300−222−22−2−226−6−66−666−600000000000000000000000000000000
χ894-4-4444-4-4-2000022-2-22-2222−22−2222−222222−2200000000000000−232323−2300−222−22−2−22−666−66−6−6600000000000000000000000000000000
χ904-4-4444-4-4-2000022-2-22-22−222222−2222−22−22220000000000000023−23−2323002−2−22−222−2−666−66−6−6600000000000000000000000000000000
χ914-4-4444-4-4-2000022-2-22-22−222222−2222−22−222200000000000000−232323−23002−2−22−222−26−6−66−666−600000000000000000000000000000000
χ924-4-4-44-444444-4-4-4-4-444-4400000000000000004400000000-4-4000000000000000000000000000000000000000000000000
χ934-4-4-44-444-244-4-4222-2-22-20000000000000000-2-200000000220000000023−23−232323−23−232300000000000000000000000000000000
χ944-4-4-44-444-244-4-4222-2-22-20000000000000000-2-2000000002200000000−232323−23−232323−2300000000000000000000000000000000
χ954-4-4-44-444-2-4-444222-2-22-24-44-4-44-44000000002200000000-2-2-222-2-222-20000000000000000000000000000000000000000
χ964-4-4-44-444-2-4-444222-2-22-2-44-444-44-4000000002200000000-2-22-2-222-2-220000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.