Finite Group Databasebeta

← Group #10693872

Character table — Group #10693872

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
χ91-1111-1-1-11-1-1-11111-1-1-1-1111-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101-1111-1-1-11-1-1-11111-1-1-1-1111-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111-1111-1-1-11-1-1-11111-1-1-1-1111-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121-1111-1-1-11-1-1-11111-1-1-1-1111-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131-1111-1-1-11-1-1-11111-1-1-1-1111-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141-1111-1-1-11-1-1-11111-1-1-1-1111-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151-1111-1-1-11-1-1-11111-1-1-1-1111-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161-1111-1-1-11-1-1-11111-1-1-1-1111-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ1722222222222-2-2-222-22222222-2-20000000022-2-222-2-2-2-2-2-200000000000000000000000000002-22-2000000000000
χ1822222222222-2-2-222-22222222-2-20000000022-2-222-2-2-2-2-2-20000000000000000000000000000-22-22000000000000
χ19222222222-2-2222-2-222222222-2-222-2-222-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-2-2222-2-222222222-2-2-2-222-2-222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-222-2-2-2-222-2-2000000000000000000000000000000002i−2i2i−2i00000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-222-2-2-2-222-2-200000000000000000000000000000000−2i2i−2i2i00000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ2722222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-222-2-222-2-2111111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-222-2-222-2-2111111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-2-2-222-2-222111111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-2-2-222-2-222111111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ31222-2-2-2-2220022-200-22-2-22-2-2200002-2002-20000002-2002-2000022-2-2000022-2-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ32222-2-2-2-2220022-200-22-2-22-2-2200002-2002-20000002-2002-2000022-2-2000022-2-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ33222-2-2-2-2220022-200-22-2-22-2-220000-2200-220000002-2002-20000-2-2220000-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ34222-2-2-2-2220022-200-22-2-22-2-220000-2200-220000002-2002-20000-2-2220000-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ352-2222-2-2-22222-2-2-2-22-2-2-2222-22-200000000-2-2222222-2-2-2-2000000000000000000000000000000002-2-2200000000
χ362-2222-2-2-22222-2-2-2-22-2-2-2222-22-200000000-2-2222222-2-2-2-200000000000000000000000000000000-222-200000000
χ372-2222-2-2-2222-222-2-2-2-2-2-2222-2-2222-2-2-2-222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ382-2222-2-2-2222-222-2-2-2-2-2-2222-2-22-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ392-2222-2-2-22-2-22-2-2222-2-2-2222-2-220000000022-2-2-2-22222-2-200000000000000000000000000002i−2i−2i2i000000000000
χ402-2222-2-2-22-2-22-2-2222-2-2-2222-2-220000000022-2-2-2-22222-2-20000000000000000000000000000−2i2i2i−2i000000000000
χ412-2222-2-2-2-122-222-2-2-2111-1-1-11-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100003−3−333−3−330000000000000000
χ422-2222-2-2-2-122-222-2-2-2111-1-1-11-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-10000−333−3−333−30000000000000000
χ432-2222-2-2-2-122-222-2-2-2111-1-1-11-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−30000000000000000
χ442-2222-2-2-2-122-222-2-2-2111-1-1-11-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−330000000000000000
χ452-2222-2-2-2-1-2-2-22222-2111-1-1-112-22222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ462-2222-2-2-2-1-2-2-22222-2111-1-1-112-22222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ472-2222-2-2-2-1-2-2-22222-2111-1-1-112-2-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ482-2222-2-2-2-1-2-2-22222-2111-1-1-112-2-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ492-22-2-222-2200-22-2002-2222-2-2-200002-200-22000000-22002-2000022-2-20000-2-22200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ502-22-2-222-2200-22-2002-2222-2-2-200002-200-22000000-22002-2000022-2-20000-2-22200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ512-22-2-222-2200-22-2002-2222-2-2-20000-22002-2000000-22002-20000-2-222000022-2-200000000000000000000−i2i2i2−i2i2−i2−i2i2
χ522-22-2-222-2200-22-2002-2222-2-2-20000-22002-2000000-22002-20000-2-222000022-2-200000000000000000000i2−i2−i2i2−i2i2i2−i2
χ5344444444-244-4-4-444-4-2-2-2-2-2-2-2-4-400000000-2-222-2-222222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022-2-22222-2-22200000000000000000000000000000000000000000000
χ55444-4-4-4-44400-4-440044-4-44-4-440000000000000000-4400-4400000000000000000000000000000000000000000000
χ56444-4-4-4-44-20044-400-4-222-222-200004-4004-4000000-2200-220000-2-2220000-2-2220000000000000000000000000000
χ57444-4-4-4-44-20044-400-4-222-222-20000-4400-44000000-2200-22000022-2-2000022-2-20000000000000000000000000000
χ58444-4-4-4-44-200-4-44004-222-222-200000000000000002-2002-2−2i3−2i32i32i30000−2i3−2i32i32i300000000000000000000000000000000
χ59444-4-4-4-44-200-4-44004-222-222-200000000000000002-2002-22i32i3−2i3−2i300002i32i3−2i3−2i300000000000000000000000000000000
χ6044-44-44-4-440000000044-4-44-4-40022−220022−220000000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ6144-44-44-4-440000000044-4-44-4-400−222200−222200000000000000−2222−22220000−2222−222200000000000000000000000000000000
χ6244-44-44-4-4-200000000-2-222-2220022−220022−220000−2i32i30000−2i32i300−22−22i6−i6i6−i6−22−22i6−i6i6−i60000000000000000000000000000
χ6344-44-44-4-4-200000000-2-222-2220022−220022−2200002i3−2i300002i3−2i300−22−22−i6i6−i6i6−22−22−i6i6−i6i60000000000000000000000000000
χ6444-44-44-4-4-200000000-2-222-22200−222200−22220000−2i32i30000−2i32i3002−22−2−i6i6−i6i62−22−2−i6i6−i6i60000000000000000000000000000
χ6544-44-44-4-4-200000000-2-222-22200−222200−222200002i3−2i300002i3−2i3002−22−2i6−i6i6−i62−22−2i6−i6i6−i60000000000000000000000000000
χ6644-4-44-44-444-40004-404-44-4-44-400000000004-4004-400000000000000000000000000000000000000000000000000
χ6744-4-44-44-44-44000-4404-44-4-44-40000000000-4400-4400000000000000000000000000000000000000000000000000
χ6844-4-44-44-4-24-40004-40-22-222-220000000000-2200-22000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ6944-4-44-44-4-24-40004-40-22-222-220000000000-2200-22000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ7044-4-44-44-4-2-44000-440-22-222-2200000000002-2002-2000000i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ7144-4-44-44-4-2-44000-440-22-222-2200000000002-2002-2000000−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ724-4444-4-4-4-2444-4-4-4-44222-2-2-224-40000000022-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ734-4444-4-4-4-2-4-44-4-4444222-2-2-22-4400000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000
χ744-44-4-444-44004-4400-4-4444-4-4-400000000000000004-400-4400000000000000000000000000000000000000000000
χ754-44-4-444-4-2004-4400-42-2-2-22220000000000000000-22002-2−2i3−2i32i32i300002i32i3−2i3−2i300000000000000000000000000000000
χ764-44-4-444-4-2004-4400-42-2-2-22220000000000000000-22002-22i32i3−2i3−2i30000−2i3−2i32i32i300000000000000000000000000000000
χ774-44-4-444-4-200-44-40042-2-2-222200004-400-440000002-200-220000-2-222000022-2-20000000000000000000000000000
χ784-44-4-444-4-200-44-40042-2-2-22220000-44004-40000002-200-22000022-2-20000-2-2220000000000000000000000000000
χ794-4-44-4-444400000000-4-44-44-440022−2200−22220000000000000022−2222−220000−2222−222200000000000000000000000000000000
χ804-4-44-4-444400000000-4-44-44-4400−22220022−2200000000000000−2222−2222000022−2222−2200000000000000000000000000000000
χ814-4-44-4-444-20000000022-22-22-20022−2200−22220000−2i32i300002i3−2i300−22−22i6−i6i6−i62−22−2−i6i6−i6i60000000000000000000000000000
χ824-4-44-4-444-20000000022-22-22-20022−2200−222200002i3−2i30000−2i32i300−22−22−i6i6−i6i62−22−2i6−i6i6−i60000000000000000000000000000
χ834-4-44-4-444-20000000022-22-22-200−22220022−220000−2i32i300002i3−2i3002−22−2−i6i6−i6i6−22−22i6−i6i6−i60000000000000000000000000000
χ844-4-44-4-444-20000000022-22-22-200−22220022−2200002i3−2i30000−2i32i3002−22−2i6−i6i6−i6−22−22−i6i6−i6i60000000000000000000000000000
χ854-4-4-444-4444-4000-440-44-4-4-4440000000000-44004-400000000000000000000000000000000000000000000000000
χ864-4-4-444-444-440004-40-44-4-4-44400000000004-400-4400000000000000000000000000000000000000000000000000
χ874-4-4-444-44-24-4000-4402-2222-2-200000000002-200-22000000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ884-4-4-444-44-24-4000-4402-2222-2-200000000002-200-22000000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ894-4-4-444-44-2-440004-402-2222-2-20000000000-22002-2000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ904-4-4-444-44-2-440004-402-2222-2-20000000000-22002-2000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000000

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