Finite Group Databasebeta

← Group #10693574

Character table — Group #10693574

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222222344444444666666644888888881212121212121212121212122424242424242424242424242424242422446666121212124444888888888888
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
χ91-1111-1-1-1111-1-1-111-1-1-1-1111-11-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1
χ101-1111-1-1-1111-1-1-111-1-1-1-1111-11-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−i−i−iii-1-111−i−iii-1-111
χ111-1111-1-1-1111-1-1-111-1-1-1-1111-11-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iiiii−i−i11-1-1−i−iii-1-111
χ121-1111-1-1-1111-1-1-111-1-1-1-1111-11-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iii−i−iii-1-111ii−i−i11-1-1
χ131-1111-1-1-1111-1-1-111-1-1-1-1111-11-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iiiii−i−i-1-111ii−i−i-1-111
χ141-1111-1-1-1111-1-1-111-1-1-1-1111-11-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iii−i−iii11-1-1−i−iii11-1-1
χ151-1111-1-1-1111-1-1-111-1-1-1-1111-11-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−iii−i−i-1-111−i−iii11-1-1
χ161-1111-1-1-1111-1-1-111-1-1-1-1111-11-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−i−i−iii11-1-1ii−i−i-1-111
χ172222222222-22-2-22-222222222-2-20000000022-2-2-2-222-2-2-2-200000000000000000000000000002-22-2000000000000
χ182222222222-22-2-22-222222222-2-20000000022-2-2-2-222-2-2-2-20000000000000000000000000000-22-22000000000000
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
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-222-2-2000000000000000000000000000000002i−2i2i−2i00000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-222-2-200000000000000000000000000000000−2i2i−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
χ2722222222-1-22-222-22-2-1-1-1-1-1-1-1-2-222-2-222-2-211-1-1111111-1-1-1-1-1-11111-1-1-1-111110000−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
χ31222-2-22-2-220202-20-202-2-22-2-2200002-2002-2002-20000002-2000022-2-2000022-2-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ32222-2-22-2-220202-20-202-2-22-2-2200002-2002-2002-20000002-2000022-2-2000022-2-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ33222-2-22-2-220202-20-202-2-22-2-220000-2200-22002-20000002-20000-2-2220000-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ34222-2-22-2-220202-20-202-2-22-2-220000-2200-22002-20000002-20000-2-2220000-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ352-2222-2-2-222-2-2222-2-2-2-2-2222-2-220000000022-2-2-2-2-2-2222200000000000000000000000000002i−2i−2i2i000000000000
χ362-2222-2-2-222-2-2222-2-2-2-2-2222-2-220000000022-2-2-2-2-2-222220000000000000000000000000000−2i2i2i−2i000000000000
χ372-2222-2-2-22-222-2-2-222-2-2-2222-2-222i2i−2i−2i−2i−2i2i2i-2-222-2-22222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ382-2222-2-2-22-222-2-2-222-2-2-2222-2-22−2i−2i2i2i2i2i−2i−2i-2-222-2-22222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ392-2222-2-2-22-2-2222-2-22-2-2-2222-22-200000000-2-2-2-22222-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ402-2222-2-2-22-2-2222-2-22-2-2-2222-22-200000000-2-2-2-22222-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ412-2222-2-2-2-122-2-2-222-2111-1-1-112-22i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-1111111−i−i−i−i−i−i−i−iiiiiiiii2-22i−2i-1-111−i−iii0000000000000000
χ422-2222-2-2-2-122-2-2-222-2111-1-1-112-22i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-1111111−i−i−i−i−i−i−i−iiiiiiiii-22−2i2i11-1-1ii−i−i0000000000000000
χ432-2222-2-2-2-122-2-2-222-2111-1-1-112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-1111111iiiiiiii−i−i−i−i−i−i−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ442-2222-2-2-2-122-2-2-222-2111-1-1-112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-1111111iiiiiiii−i−i−i−i−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
χ452-2222-2-2-2-1-222-2-2-222111-1-1-11-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i0000−i3i3i3−i33−3−330000000000000000
χ462-2222-2-2-2-1-222-2-2-222111-1-1-11-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i0000i3−i3−i3i3−333−30000000000000000
χ472-2222-2-2-2-1-222-2-2-222111-1-1-11-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii0000−i3i3i3−i3−333−30000000000000000
χ482-2222-2-2-2-1-222-2-2-222111-1-1-11-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii0000i3−i3−i3i33−3−330000000000000000
χ492-22-2-2-2222020-220-20-2222-2-2-200002i−2i00−2i2i002-2000000-2200002i2i−2i−2i0000−2i−2i2i2i000000000000000000002−2−22−i2i2i2−i2
χ502-22-2-2-2222020-220-20-2222-2-2-200002i−2i00−2i2i002-2000000-2200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000−222−2i2−i2−i2i2
χ512-22-2-2-2222020-220-20-2222-2-2-20000−2i2i002i−2i002-2000000-220000−2i−2i2i2i00002i2i−2i−2i000000000000000000002−2−22i2−i2−i2i2
χ522-22-2-2-2222020-220-20-2222-2-2-20000−2i2i002i−2i002-2000000-220000−2i−2i2i2i00002i2i−2i−2i00000000000000000000−222−2−i2i2i2−i2
χ5344444444-24-44-4-44-44-2-2-2-2-2-2-2-4-400000000-2-22222-2-2222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244000000002222-2-222-2-22200000000000000000000000000000000000000000000
χ55444-4-44-4-440-40-440404-4-44-4-44000000000000-44000000-4400000000000000000000000000000000000000000000
χ56444-4-44-4-4-20404-40-40-222-222-200004-4004-400-22000000-220000-2-2220000-2-2220000000000000000000000000000
χ57444-4-44-4-4-20404-40-40-222-222-20000-4400-4400-22000000-22000022-2-2000022-2-20000000000000000000000000000
χ58444-4-44-4-4-20-40-44040-222-222-20000000000002-20000002-2−2i3−2i32i32i30000−2i3−2i32i32i300000000000000000000000000000000
χ59444-4-44-4-4-20-40-44040-222-222-20000000000002-20000002-22i32i3−2i3−2i300002i32i3−2i3−2i300000000000000000000000000000000
χ6044-44-4-44-440000000044-4-44-4-400−2i22i200−2i22i200000000000000−2i22i2−2i22i20000−2i22i2−2i22i200000000000000000000000000000000
χ6144-44-4-44-440000000044-4-44-4-4002i2−2i2002i2−2i2000000000000002i2−2i22i2−2i200002i2−2i22i2−2i200000000000000000000000000000000
χ6244-44-4-44-4-200000000-2-222-22200−2i22i200−2i22i2000000−2i32i300−2i32i300i2−i2i2−i26−66−6i2−i2i2−i26−66−60000000000000000000000000000
χ6344-44-4-44-4-200000000-2-222-22200−2i22i200−2i22i20000002i3−2i3002i3−2i300i2−i2i2−i2−66−66i2−i2i2−i2−66−660000000000000000000000000000
χ6444-44-4-44-4-200000000-2-222-222002i2−2i2002i2−2i2000000−2i32i300−2i32i300−i2i2−i2i2−66−66−i2i2−i2i2−66−660000000000000000000000000000
χ6544-44-4-44-4-200000000-2-222-222002i2−2i2002i2−2i20000002i3−2i3002i3−2i300−i2i2−i2i26−66−6−i2i2−i2i26−66−60000000000000000000000000000
χ6644-4-44-4-44440400-40-44-44-4-44-400000000004-400004-4000000000000000000000000000000000000000000000000
χ6744-4-44-4-444-40-4004044-44-4-44-40000000000-440000-44000000000000000000000000000000000000000000000000
χ6844-4-44-4-44-240400-40-4-22-222-220000000000-220000-2200006−6−666−6−666−6−666−6−660000000000000000000000000000
χ6944-4-44-4-44-240400-40-4-22-222-220000000000-220000-220000−666−6−666−6−666−6−666−60000000000000000000000000000
χ7044-4-44-4-44-2-40-400404-22-222-2200000000002-200002-200006−6−66−666−66−6−66−666−60000000000000000000000000000
χ7144-4-44-4-44-2-40-400404-22-222-2200000000002-200002-20000−666−66−6−66−666−66−6−660000000000000000000000000000
χ724-4444-4-4-4-24-4-4444-4-4222-2-2-22-4400000000-2-2222222-2-2-2-200000000000000000000000000000000000000000000
χ734-4444-4-4-4-2-4-4444-4-44222-2-2-224-4000000002222-2-2-2-222-2-200000000000000000000000000000000000000000000
χ744-44-4-4-44440-404-4040-4444-4-4-4000000000000-440000004-400000000000000000000000000000000000000000000
χ754-44-4-4-444-2040-440-402-2-2-222200004i−4i00−4i4i00-220000002-20000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000
χ764-44-4-4-444-2040-440-402-2-2-22220000−4i4i004i−4i00-220000002-200002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000
χ774-44-4-4-444-20-404-40402-2-2-22220000000000002-2000000-222323−23−230000−23−23232300000000000000000000000000000000
χ784-44-4-4-444-20-404-40402-2-2-22220000000000002-2000000-22−23−23232300002323−23−2300000000000000000000000000000000
χ794-4-44-44-44400000000-4-44-44-440022−2200−22220000000000000022−2222−220000−2222−222200000000000000000000000000000000
χ804-4-44-44-44400000000-4-44-44-4400−22220022−2200000000000000−2222−2222000022−2222−2200000000000000000000000000000000
χ814-4-44-44-44-20000000022-22-22-20022−2200−2222000000−2i32i3002i3−2i300−22−22i6−i6i6−i62−22−2−i6i6−i6i60000000000000000000000000000
χ824-4-44-44-44-20000000022-22-22-20022−2200−22220000002i3−2i300−2i32i300−22−22−i6i6−i6i62−22−2i6−i6i6−i60000000000000000000000000000
χ834-4-44-44-44-20000000022-22-22-200−22220022−22000000−2i32i3002i3−2i3002−22−2−i6i6−i6i6−22−22i6−i6i6−i60000000000000000000000000000
χ844-4-44-44-44-20000000022-22-22-200−22220022−220000002i3−2i300−2i32i3002−22−2i6−i6i6−i6−22−22−i6i6−i6i60000000000000000000000000000
χ854-4-4-4444-4440-400-404-44-4-4-44400000000004-40000-44000000000000000000000000000000000000000000000000
χ864-4-4-4444-44-4040040-4-44-4-4-4440000000000-4400004-4000000000000000000000000000000000000000000000000
χ874-4-4-4444-4-240-400-4042-2222-2-20000000000-2200002-20000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ884-4-4-4444-4-240-400-4042-2222-2-20000000000-2200002-20000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ894-4-4-4444-4-2-4040040-42-2222-2-200000000002-20000-220000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ904-4-4-4444-4-2-4040040-42-2222-2-200000000002-20000-220000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000

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