Finite Group Databasebeta

← Group #10697810

Character table — Group #10697810

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212124444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ92222222222-2-2222-2-22222222-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222-2-2222-2-22222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ11222222222-222-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-2000000000000000000000000000022-2-2000000000000
χ12222222222-222-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000000000000-2-222000000000000
χ13222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-2000000000000000000000000000000002i2i−2i−2i00000000
χ14222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000000000000000−2i−2i2i2i00000000
χ1522222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ1622222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ1722222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ1822222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ1922222222-12-2-2222-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111110000−i3−i3i3i3−i3−i3i3i30000000000000000
χ2022222222-12-2-2222-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111110000i3i3−i3−i3i3i3−i3−i30000000000000000
χ2122222222-12-2-2222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i30000000000000000
χ2222222222-12-2-2222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i30000000000000000
χ23222-2-22-2-222002-2-20022-2-22-2-200000022-2-22-2000000002-2000000002222-2-2-2-20000000000000000000022−2−222−2−2
χ24222-2-22-2-222002-2-20022-2-22-2-200000022-2-22-2000000002-2000000002222-2-2-2-200000000000000000000−2−222−2−222
χ25222-2-22-2-222002-2-20022-2-22-2-2000000-2-2222-2000000002-200000000-2-2-2-222220000000000000000000022−2−2−2−222
χ26222-2-22-2-222002-2-20022-2-22-2-2000000-2-2222-2000000002-200000000-2-2-2-2222200000000000000000000−2−22222−2−2
χ2722-22-2-22-22022000-2-22-22-2-22-20022−2−22−22−20022-2-20000002222−2−2−2−222−2−222−2−20000000000002-2002−22−200000000
χ2822-22-2-22-22022000-2-22-22-2-22-20022−2−22−22−20022-2-20000002222−2−2−2−222−2−222−2−2000000000000-2200−22−2200000000
χ2922-22-2-22-22022000-2-22-22-2-22-200−2−222−22−220022-2-2000000−2−2−2−22222−2−222−2−2220000000000002-200−22−2200000000
χ3022-22-2-22-22022000-2-22-22-2-22-200−2−222−22−220022-2-2000000−2−2−2−22222−2−222−2−222000000000000-22002−22−200000000
χ3122-22-2-22-220-2-2000222-22-2-22-20022−2−2−22−2200-2-2220000002222−2−2−2−2−2−222−2−222000000000000002i−2i−i2i2i2−i200000000
χ3222-22-2-22-220-2-2000222-22-2-22-20022−2−2−22−2200-2-2220000002222−2−2−2−2−2−222−2−22200000000000000−2i2ii2−i2−i2i200000000
χ3322-22-2-22-220-2-2000222-22-2-22-200−2−2222−22−200-2-222000000−2−2−2−2222222−2−222−2−2000000000000002i−2ii2−i2−i2i200000000
χ3422-22-2-22-220-2-2000222-22-2-22-200−2−2222−22−200-2-222000000−2−2−2−2222222−2−222−2−200000000000000−2i2i−i2i2i2−i200000000
χ352-2-2222-2-22200-22-200-2-2222-2-2002-22-200002-200000000-2222-2-222-2-200000000000000000000000000002−22−22−22−2
χ362-2-2222-2-22200-22-200-2-2222-2-2002-22-200002-200000000-2222-2-222-2-20000000000000000000000000000−22−22−22−22
χ372-2-2222-2-22200-22-200-2-2222-2-200-22-2200002-200000000-22-2-222-2-22200000000000000000000000000002−22−2−22−22
χ382-2-2222-2-22200-22-200-2-2222-2-200-22-2200002-200000000-22-2-222-2-2220000000000000000000000000000−22−222−22−2
χ392-2-2-2-2222222-2-2-222-2-2-2-2-22222-200000000222-22-222-2-2-2-200000000000000000000000000000000000000002-2-22
χ402-2-2-2-2222222-2-2-222-2-2-2-2-22222-200000000222-22-222-2-2-2-20000000000000000000000000000000000000000-222-2
χ412-2-2-2-222222-22-2-22-22-2-2-2-2222-220000000022-22-22-2-222-2-20000000000000000000000000000000000002-2-220000
χ422-2-2-2-222222-22-2-22-22-2-2-2-2222-220000000022-22-22-2-222-2-2000000000000000000000000000000000000-222-20000
χ432-2-2-2-22222-22-222-22-2-2-2-2-2222-2200000000-2-22-22-2-2-222220000000000000000002-200002-22-20000000000000000
χ442-2-2-2-22222-22-222-22-2-2-2-2-2222-2200000000-2-22-22-2-2-22222000000000000000000-220000-22-220000000000000000
χ452-2-2-2-22222-2-2222-2-22-2-2-2-22222-200000000-2-2-22-2222-2-22200000000000000002-2002-22-200000000000000000000
χ462-2-2-2-22222-2-2222-2-22-2-2-2-22222-200000000-2-2-22-2222-2-2220000000000000000-2200-22-2200000000000000000000
χ472-2-2-2-2222-1-22-222-22-21111-1-1-1-220000000011-11-1111-1-1-1-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3002-2−i3i3i3−i3-11-110000000000000000
χ482-2-2-2-2222-1-22-222-22-21111-1-1-1-220000000011-11-1111-1-1-1-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300-22i3−i3−i3i31-11-10000000000000000
χ492-2-2-2-2222-1-22-222-22-21111-1-1-1-220000000011-11-1111-1-1-1-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3002-2i3−i3−i3i3-11-110000000000000000
χ502-2-2-2-2222-1-22-222-22-21111-1-1-1-220000000011-11-1111-1-1-1-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300-22−i3i3i3−i31-11-10000000000000000
χ512-2-2-2-2222-1-2-2222-2-221111-1-1-12-200000000111-11-1-1-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i32-200-11-11−i3i3i3−i30000000000000000
χ522-2-2-2-2222-1-2-2222-2-221111-1-1-12-200000000111-11-1-1-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3-22001-11-1i3−i3−i3i30000000000000000
χ532-2-2-2-2222-1-2-2222-2-221111-1-1-12-200000000111-11-1-1-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i32-200-11-11i3−i3−i3i30000000000000000
χ542-2-2-2-2222-1-2-2222-2-221111-1-1-12-200000000111-11-1-1-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3-22001-11-1−i3i3i3−i30000000000000000
χ5544444444-2-444-4-4-444-2-2-2-2-2-2-2-4-40000000022-2-2-2-222222200000000000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222-2-2-2-22200000000000000000000000000000000000000000000
χ57444-4-44-4-44-400-4440044-4-44-4-40000000000-4400000000-4400000000000000000000000000000000000000000000
χ58444-4-44-4-4-24004-4-400-2-222-22200000044-4-4-2200000000-2200000000-2-2-2-222220000000000000000000000000000
χ59444-4-44-4-4-24004-4-400-2-222-222000000-4-444-2200000000-22000000002222-2-2-2-20000000000000000000000000000
χ60444-4-44-4-4-2-400-44400-2-222-22200000000002-2000000002-2−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000
χ61444-4-44-4-4-2-400-44400-2-222-22200000000002-2000000002-22i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000
χ6244-44-4-44-4-2044000-4-4-22-222-22002222−22−2222−2222−2200-2-222000000−2−2−2−22222−2−222−2−2220000000000000000000000000000
χ6344-44-4-44-4-2044000-4-4-22-222-2200−22−222222−2222−222200-2-2220000002222−2−2−2−222−2−222−2−20000000000000000000000000000
χ6444-44-4-44-4-20-4-400044-22-222-22002222−22−22−2222−22220022-2-2000000−2−2−2−2222222−2−222−2−20000000000000000000000000000
χ6544-44-4-44-4-20-4-400044-22-222-2200−22−22222222−2222−220022-2-20000002222−2−2−2−2−2−222−2−2220000000000000000000000000000
χ6644-4-44-4-444000000004-4-44-4-4400000022−22−2222000000000000000000002222−22−22−22−2222220000000000000000000000000000
χ6744-4-44-4-444000000004-4-44-4-44000000−222222−2200000000000000000000−22−2222222222−22−220000000000000000000000000000
χ6844-4-44-4-44-200000000-222-222-200000022−22−2222000000−2i32i3−2i32i300i6−i6−i6i6−i6i6i6−i6−2−22222−2−20000000000000000000000000000
χ6944-4-44-4-44-200000000-222-222-200000022−22−22220000002i3−2i32i3−2i300−i6i6i6−i6i6−i6−i6i6−2−22222−2−20000000000000000000000000000
χ7044-4-44-4-44-200000000-222-222-2000000−222222−22000000−2i32i3−2i32i300−i6i6i6−i6i6−i6−i6i622−2−2−2−2220000000000000000000000000000
χ7144-4-44-4-44-200000000-222-222-2000000−222222−220000002i3−2i32i3−2i300i6−i6−i6i6−i6i6i6−i622−2−2−2−2220000000000000000000000000000
χ724-444-4-4-44400000000-444-4-4-440022−22−222200000000000000002222−22−22−22−222222000000000000000000000000000000000000
χ734-444-4-4-44400000000-444-4-4-4400−222222−220000000000000000−22−2222222222−22−22000000000000000000000000000000000000
χ744-444-4-4-44-2000000002-2-2222-20022−22−22220000000000−2i32i32i3−2i300−2−22222−2−2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ754-444-4-4-44-2000000002-2-2222-20022−22−222200000000002i3−2i3−2i32i300−2−22222−2−2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ764-444-4-4-44-2000000002-2-2222-200−222222−220000000000−2i32i32i3−2i30022−2−2−2−222i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ774-444-4-4-44-2000000002-2-2222-200−222222−2200000000002i3−2i3−2i32i30022−2−2−2−222−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ784-44-44-44-4404-4000-44-44-44-44-40000000000004-4-4400000000000000000000000000000000000000000000000000
χ794-44-44-44-440-440004-4-44-44-44-4000000000000-444-400000000000000000000000000000000000000000000000000
χ804-44-44-44-4-204-4000-442-22-22-22000000000000-222-2000000i6−i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ814-44-44-44-4-204-4000-442-22-22-22000000000000-222-2000000−i6i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ824-44-44-44-4-20-440004-42-22-22-220000000000002-2-22000000i6−i6i6−i6−i6i6−i6i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ834-44-44-44-4-20-440004-42-22-22-220000000000002-2-22000000−i6i6−i6i6i6−i6i6−i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ844-4-4444-4-44-4004-4400-4-4444-4-40000000000-44000000004-400000000000000000000000000000000000000000000
χ854-4-4444-4-4-2400-44-40022-2-2-222004-44-40000-22000000002-2-2-222-2-222000000000000000000000000000000000000
χ864-4-4444-4-4-2400-44-40022-2-2-22200-44-440000-22000000002-222-2-222-2-2000000000000000000000000000000000000
χ874-4-4444-4-4-2-4004-440022-2-2-22200000000002-200000000-2200000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000
χ884-4-4444-4-4-2-4004-440022-2-2-22200000000002-200000000-22000000002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000
χ894-4-4-4-4444-244-4-4-444-42222-2-2-24-400000000-2-2-22-22-2-2222200000000000000000000000000000000000000000000
χ904-4-4-4-4444-24-44-4-44-442222-2-2-2-4400000000-2-22-22-222-2-22200000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).