Finite Group Databasebeta

← Group #10693602

Character table — Group #10693602

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
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91-1-1111-1-1111-1-1-111-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−iii−i−i11-1-1i−ii−i11-1-1ii−i−i11-1-1
χ101-1-1111-1-1111-1-1-111-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−iii−i−i11-1-1−ii−ii-1-111−i−iii-1-111
χ111-1-1111-1-1111-1-1-111-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii−i−iii-1-111i−ii−i11-1-1−i−iii-1-111
χ121-1-1111-1-1111-1-1-111-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii−i−iii-1-111−ii−ii-1-111ii−i−i11-1-1
χ131-1-1111-1-1111-1-1-111-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii−i−iii11-1-1i−ii−i-1-111ii−i−i-1-111
χ141-1-1111-1-1111-1-1-111-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii−i−iii11-1-1−ii−ii11-1-1−i−iii11-1-1
χ151-1-1111-1-1111-1-1-111-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−iii−i−i-1-111i−ii−i-1-111−i−iii11-1-1
χ161-1-1111-1-1111-1-1-111-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−iii−i−i-1-111−ii−ii11-1-1ii−i−i-1-111
χ172222222222-22-2-22-222222222-2-20000000022-2-222-2-2-2-2-2-2000000000000000000000000000022-2-2000000000000
χ182222222222-22-2-22-222222222-2-20000000022-2-222-2-2-2-2-2-20000000000000000000000000000-2-222000000000000
χ19222222222-22-222-22-22222222-2-222-2-222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-22-222-22-22222222-2-2-2-222-2-222-2-222-2-2-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-2000000000000000000000000000000002i−2i2i−2i00000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000000000000000−2i2i−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
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-21111-1-1-1-10000000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222-1-1-1-111110000000000000000
χ2722222222-1-22-222-22-2-1-1-1-1-1-1-1-2-222-2-222-2-211-1-1111111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-1-22-222-22-2-1-1-1-1-1-1-1-2-222-2-222-2-211-1-1111111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-1-22-222-22-2-1-1-1-1-1-1-1-2-2-2-222-2-22211-1-1111111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-1-22-222-22-2-1-1-1-1-1-1-1-2-2-2-222-2-22211-1-1111111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-2-2-220202-20-2022-22-2-2-200002-2002-2002-20000002-2000022-2-2000022-2-2000000000000000000002−22−22−22−2
χ322222-2-2-2-220202-20-2022-22-2-2-200002-2002-2002-20000002-2000022-2-2000022-2-200000000000000000000−22−22−22−22
χ332222-2-2-2-220202-20-2022-22-2-2-20000-2200-22002-20000002-20000-2-2220000-2-222000000000000000000002−22−2−22−22
χ342222-2-2-2-220202-20-2022-22-2-2-20000-2200-22002-20000002-20000-2-2220000-2-22200000000000000000000−22−222−22−2
χ352-2-2222-2-222-2-2222-2-2-2-2-222-22-220000000022-2-2-2-2-2-2222200000000000000000000000000002i−2i−2i2i000000000000
χ362-2-2222-2-222-2-2222-2-2-2-2-222-22-220000000022-2-2-2-2-2-222220000000000000000000000000000−2i2i2i−2i000000000000
χ372-2-2222-2-22-222-2-2-222-2-2-222-22-222i2i−2i−2i−2i−2i2i2i-2-22222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ382-2-2222-2-22-222-2-2-222-2-2-222-22-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ392-2-2222-2-22-2-2222-2-22-2-2-222-222-200000000-2-2-2-22222-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ402-2-2222-2-22-2-2222-2-22-2-2-222-222-200000000-2-2-2-22222-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ412-2-2222-2-2-122-2-2-222-2111-1-11-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii2-22i−2i−i−iii-1-1110000000000000000
χ422-2-2222-2-2-122-2-2-222-2111-1-11-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii-22−2i2iii−i−i11-1-10000000000000000
χ432-2-2222-2-2-122-2-2-222-2111-1-11-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i2-2−2i2iii−i−i-1-1110000000000000000
χ442-2-2222-2-2-122-2-2-222-2111-1-11-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i-222i−2i−i−iii11-1-10000000000000000
χ452-2-2222-2-2-1-222-2-2-222111-1-11-1-222i2i−2i−2i−2i−2i2i2i11-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00003−3−33−i3i3i3−i30000000000000000
χ462-2-2222-2-2-1-222-2-2-222111-1-11-1-222i2i−2i−2i−2i−2i2i2i11-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i0000−333−3i3−i3−i3i30000000000000000
χ472-2-2222-2-2-1-222-2-2-222111-1-11-1-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00003−3−33i3−i3−i3i30000000000000000
χ482-2-2222-2-2-1-222-2-2-222111-1-11-1-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii0000−333−3−i3i3i3−i30000000000000000
χ492-2-22-2-2222020-220-20-2-222-22-200002i−2i00−2i2i002-2000000-2200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000−i2i2i2−i2−222−2
χ502-2-22-2-2222020-220-20-2-222-22-200002i−2i00−2i2i002-2000000-2200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000i2−i2−i2i22−2−22
χ512-2-22-2-2222020-220-20-2-222-22-20000−2i2i002i−2i002-2000000-220000−2i−2i2i2i00002i2i−2i−2i00000000000000000000−i2i2i2−i22−2−22
χ522-2-22-2-2222020-220-20-2-222-22-20000−2i2i002i−2i002-2000000-220000−2i−2i2i2i00002i2i−2i−2i00000000000000000000i2−i2−i2i2−222−2
χ5344444444-24-44-4-44-44-2-2-2-2-2-2-2-4-400000000-2-222-2-222222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222-2-2-2-22200000000000000000000000000000000000000000000
χ554444-4-4-4-440-40-4404044-44-4-4-4000000000000-44000000-4400000000000000000000000000000000000000000000
χ564444-4-4-4-4-20404-40-40-2-22-222200004-4004-400-22000000-220000-2-2220000-2-2220000000000000000000000000000
χ574444-4-4-4-4-20404-40-40-2-22-22220000-4400-4400-22000000-22000022-2-2000022-2-20000000000000000000000000000
χ584444-4-4-4-4-20-40-44040-2-22-22220000000000002-20000002-2−2i3−2i32i32i30000−2i3−2i32i32i300000000000000000000000000000000
χ594444-4-4-4-4-20-40-44040-2-22-22220000000000002-20000002-22i32i3−2i3−2i300002i32i3−2i3−2i300000000000000000000000000000000
χ6044-4-44-44-4440-400-4044-44-44-4-400000000004-4004-400000000000000000000000000000000000000000000000000
χ6144-4-44-44-44-4040040-44-44-44-4-40000000000-4400-4400000000000000000000000000000000000000000000000000
χ6244-4-44-44-4-240-400-404-22-22-2220000000000-2200-22000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i60000000000000000000000000000
χ6344-4-44-44-4-240-400-404-22-22-2220000000000-2200-22000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i60000000000000000000000000000
χ6444-4-44-44-4-2-4040040-4-22-22-22200000000002-2002-2000000i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i60000000000000000000000000000
χ6544-4-44-44-4-2-4040040-4-22-22-22200000000002-2002-2000000−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i60000000000000000000000000000
χ6644-4-4-44-444000000004-4-4-4-4440022−220022−220000000000000022−22−2222000022−22−222200000000000000000000000000000000
χ6744-4-4-44-444000000004-4-4-4-44400−222200−222200000000000000−222222−220000−222222−2200000000000000000000000000000000
χ6844-4-4-44-44-200000000-22222-2-20022−220022−2200000000−2i32i3−2i32i300−222−2i6−i6−i6i6−222−2i6−i6−i6i60000000000000000000000000000
χ6944-4-4-44-44-200000000-22222-2-20022−220022−22000000002i3−2i32i3−2i300−222−2−i6i6i6−i6−222−2−i6i6i6−i60000000000000000000000000000
χ7044-4-4-44-44-200000000-22222-2-200−222200−222200000000−2i32i3−2i32i3002−2−22−i6i6i6−i62−2−22−i6i6i6−i60000000000000000000000000000
χ7144-4-4-44-44-200000000-22222-2-200−222200−2222000000002i3−2i32i3−2i3002−2−22i6−i6−i6i62−2−22i6−i6−i6i60000000000000000000000000000
χ724-44-44-4-44440400-40-4-44-4-444-400000000004-400-4400000000000000000000000000000000000000000000000000
χ734-44-44-4-444-40-400404-44-4-444-40000000000-44004-400000000000000000000000000000000000000000000000000
χ744-44-44-4-44-240400-40-42-222-2-220000000000-22002-20000006−66−66−66−6−66−66−66−660000000000000000000000000000
χ754-44-44-4-44-240400-40-42-222-2-220000000000-22002-2000000−66−66−66−666−66−66−66−60000000000000000000000000000
χ764-44-44-4-44-2-40-4004042-222-2-2200000000002-200-220000006−66−6−66−66−66−666−66−60000000000000000000000000000
χ774-44-44-4-44-2-40-4004042-222-2-2200000000002-200-22000000−66−666−66−66−66−6−66−660000000000000000000000000000
χ784-44-4-444-4400000000-444-4-4-4400−2i22i2002i2−2i200000000000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000
χ794-44-4-444-4400000000-444-4-4-44002i2−2i200−2i22i2000000000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000
χ804-44-4-444-4-2000000002-2-2222-200−2i22i2002i2−2i200000000−2i32i32i3−2i300i2−i2−i2i26−6−66−i2i2i2−i2−666−60000000000000000000000000000
χ814-44-4-444-4-2000000002-2-2222-200−2i22i2002i2−2i2000000002i3−2i3−2i32i300i2−i2−i2i2−666−6−i2i2i2−i26−6−660000000000000000000000000000
χ824-44-4-444-4-2000000002-2-2222-2002i2−2i200−2i22i200000000−2i32i32i3−2i300−i2i2i2−i2−666−6i2−i2−i2i26−6−660000000000000000000000000000
χ834-44-4-444-4-2000000002-2-2222-2002i2−2i200−2i22i2000000002i3−2i3−2i32i300−i2i2i2−i26−6−66i2−i2−i2i2−666−60000000000000000000000000000
χ844-4-4444-4-4-24-4-4444-4-4222-2-22-2-4400000000-2-2222222-2-2-2-200000000000000000000000000000000000000000000
χ854-4-4444-4-4-2-4-4444-4-44222-2-22-24-4000000002222-2-2-2-222-2-200000000000000000000000000000000000000000000
χ864-4-44-4-44440-404-4040-4-444-44-4000000000000-440000004-400000000000000000000000000000000000000000000
χ874-4-44-4-444-2040-440-4022-2-22-2200004i−4i00−4i4i00-220000002-20000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000
χ884-4-44-4-444-2040-440-4022-2-22-220000−4i4i004i−4i00-220000002-200002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000
χ894-4-44-4-444-20-404-404022-2-22-220000000000002-2000000-222323−23−230000−23−23232300000000000000000000000000000000
χ904-4-44-4-444-20-404-404022-2-22-220000000000002-2000000-22−23−23232300002323−23−2300000000000000000000000000000000

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