Finite Group Databasebeta

← Group #10714018

Character table — Group #10714018

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222222344446666666888888884444888812121212121212121212121224242424242424242424242424242424161616161616161616161616161616162222666666662244
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
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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
χ23222-22-2-2-222-22-222-2-22-2-22222-2-2-2-2000000002-2000000002-22222-2-2-2-2000000000000000000000000000000000000002i−2i
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χ3022-2-2-22-22200002-22-2-22-222−2−222−2−200-22−2−222000000-2-2220022−2−222−2−2−2−2−2−22222ζ25−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+ζ43ζ11−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−ζ470000000000000000
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χ3422-2-2-22-22200002-22-2-22-2−2−222−2−22200-2222−2−2000000-2-22200−2−222−2−2222222−2−2−2−2−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−ζ47ζ25−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−ζ430000000000000000
χ352-22-2-2-22220000-222-2-2-222−22−22−22−22-2002−22−20022-2-20000002−22−22−22−222−2−222−2−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000000
χ362-22-2-2-22220000-222-2-2-222−22−22−22−22-2002−22−20022-2-20000002−22−22−22−222−2−222−2−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000000
χ372-22-2-2-22220000-222-2-2-222−22−22−22−2-2200−22−2200-2-2220000002−22−22−22−2−2−222−2−222−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000000
χ382-22-2-2-22220000-222-2-2-222−22−22−22−2-2200−22−2200-2-2220000002−22−22−22−2−2−222−2−222ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000000
χ392-22-2-2-22220000-222-2-2-22−22−22−22−222-200−22−220022-2-2000000−22−22−22−22−2−222−2−222ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000000
χ402-22-2-2-22220000-222-2-2-22−22−22−22−222-200−22−220022-2-2000000−22−22−22−22−2−222−2−222−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000000000
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χ422-22-2-2-22220000-222-2-2-22−22−22−22−22-22002−22−200-2-222000000−22−22−22−2222−2−222−2−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000000
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χ7044-44-4-44-4400004-4-44-4-442222−22−22−22−222222000000000000000000002222−22−22−22−2222220000000000000000000000000000000000000000
χ7144-44-4-44-4400004-4-44-4-44−22−2222222222−22−2200000000000000000000−22−2222222222−22−220000000000000000000000000000000000000000
χ7244-44-4-44-4-20000-222-222-22222−22−22−22−2222220000000000−2i32i32i3−2i3000000−2−22222−2−2−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ7344-44-4-44-4-20000-222-222-22222−22−22−22−22222200000000002i3−2i3−2i32i3000000−2−22222−2−2i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ7444-44-4-44-4-20000-222-222-2−22−2222222222−22−220000000000−2i32i32i3−2i300000022−2−2−2−222i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ7544-44-4-44-4-20000-222-222-2−22−2222222222−22−2200000000002i3−2i3−2i32i300000022−2−2−2−222−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ7644-4-4-44-44-20000-22-222-222222−22−222222−22−22004-42222−22−22000000-2-22200−2−222−2−222−2−2−2−2222200000000000000000000000000000000
χ7744-4-4-44-44-20000-22-222-222222−22−222222−22−2200-44−22−22222200000022-2-200−2−222−2−2222222−2−2−2−200000000000000000000000000000000
χ7844-4-4-44-44-20000-22-222-22−22−222222−22−222222004-4−22−222222000000-2-2220022−2−222−2−22222−2−2−2−200000000000000000000000000000000
χ7944-4-4-44-44-20000-22-222-22−22−222222−22−22222200-442222−22−2200000022-2-20022−2−222−2−2−2−2−2−2222200000000000000000000000000000000
χ804-444-44-4-440000-44-44-44-422−2222−22−2222−22220000000000000000000022−2222−22−2222−22220000000000000000000000000000000000000000
χ814-444-44-4-440000-44-44-44-4−2222−222222−2222−2200000000000000000000−2222−222222−2222−220000000000000000000000000000000000000000
χ824-444-44-4-4-200002-22-22-2222−2222−22−2222−222200000000000000−2i32i32i3−2i300−22−222−22−2−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ834-444-44-4-4-200002-22-22-2222−2222−22−2222−2222000000000000002i3−2i3−2i32i300−22−222−22−2i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ844-444-44-4-4-200002-22-22-22−2222−222222−2222−2200000000000000−2i32i32i3−2i3002−22−2−22−22i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ854-444-44-4-4-200002-22-22-22−2222−222222−2222−22000000000000002i3−2i3−2i32i3002−22−2−22−22−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ864-44-4-4-444-200002-2-2222-222−2222−2222−2222−224-40022−2222−2200-2-222000000−22−22−22−22−2−222−2−22200000000000000000000000000000000
χ874-44-4-4-444-200002-2-2222-222−2222−2222−2222−22-4400−2222−22220022-2-2000000−22−22−22−2222−2−222−2−200000000000000000000000000000000
χ884-44-4-4-444-200002-2-2222-2−2222−2222−2222−22224-400−2222−222200-2-2220000002−22−22−22−222−2−222−2−200000000000000000000000000000000
χ894-44-4-4-444-200002-2-2222-2−2222−2222−2222−2222-440022−2222−220022-2-20000002−22−22−22−2−2−222−2−22200000000000000000000000000000000
χ904-4-444-4-44-24-4-4422-2-2-2220000000000004-4-44-22000000002-200000000-2-22222-2-200000000000000000000000000000000
χ914-4-444-4-44-24-4-4422-2-2-222000000000000-444-4-22000000002-20000000022-2-2-2-22200000000000000000000000000000000
χ924-4-444-4-44-2-444-422-2-2-2224-4-444-4-44000000002-200000000-22-222-2-222-20000000000000000000000000000000000000000
χ934-4-444-4-44-2-444-422-2-2-222-444-4-444-4000000002-200000000-222-2-222-2-220000000000000000000000000000000000000000
χ944-4-4-4444-4444-4-4-4-4-4-444400000000000000004400000000-4-4000000000000000000000000000000000000000000000000
χ954-4-4-4444-4-244-4-42222-2-2-20000000000000000-2-2−2i32i3−2i32i32i3−2i32i3−2i322000000000000000000000000000000000000000000000000
χ964-4-4-4444-4-244-4-42222-2-2-20000000000000000-2-22i3−2i32i3−2i3−2i32i3−2i32i322000000000000000000000000000000000000000000000000

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