Finite Group Databasebeta

← Group #10693860

Character table — Group #10693860

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
χ91-1111-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−ii−ii−iii−i−i11-1-111-1-1
χ101-1111-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i−ii−ii−i−iii-1-111-1-111
χ111-1111-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iiii−ii−iii−i−i-1-111-1-111
χ121-1111-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii−i−iii11-1-111-1-1
χ131-1111-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iiii−ii−i−i−iii11-1-1-1-111
χ141-1111-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iii−ii−iiii−i−i-1-11111-1-1
χ151-1111-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−ii−ii−i−i−iii-1-11111-1-1
χ161-1111-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−i−ii−iiii−i−i11-1-1-1-111
χ17222222222222-2-2-2-222222222-2-20000000022-2-222-2-2-2-2-2-2000000000000000000000000000022-2-2000000000000
χ18222222222222-2-2-2-222222222-2-20000000022-2-222-2-2-2-2-2-20000000000000000000000000000-2-222000000000000
χ19222222222-2-2-22222-22222222-2-222-2-222-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-2-2-22222-22222222-2-2-2-222-2-222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
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
χ2722222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-222-2-222-2-2111111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-222-2-222-2-2111111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-222-2-222111111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-222-2-222111111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ31222-2-22-2-22000-22-2202-22-2-22-200002i−2i002i−2i0000002-2002-200002i2i−2i−2i00002i2i−2i−2i00000000000000000000−i2i2−i2i22−22−2
χ32222-2-22-2-22000-22-2202-22-2-22-200002i−2i002i−2i0000002-2002-200002i2i−2i−2i00002i2i−2i−2i00000000000000000000i2−i2i2−i2−22−22
χ33222-2-22-2-22000-22-2202-22-2-22-20000−2i2i00−2i2i0000002-2002-20000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000−i2i2−i2i2−22−22
χ34222-2-22-2-22000-22-2202-22-2-22-20000−2i2i00−2i2i0000002-2002-20000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000i2−i2i2−i22−22−2
χ352-2222-2-2-222-2-22-2-222-2-2222-2-2-220000000022-2-2-2-22222-2-200000000000000000000000000002i−2i−2i2i000000000000
χ362-2222-2-2-222-2-22-2-222-2-2222-2-2-220000000022-2-2-2-22222-2-20000000000000000000000000000−2i2i2i−2i000000000000
χ372-2222-2-2-22-2222-2-22-2-2-2222-2-22-200000000-2-2222222-2-2-2-2000000000000000000000000000000002-2-2200000000
χ382-2222-2-2-22-2222-2-22-2-2-2222-2-22-200000000-2-2222222-2-2-2-200000000000000000000000000000000-222-200000000
χ392-2222-2-2-22-222-222-2-2-2-2222-2-2-2222-2-2-2-222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ402-2222-2-2-22-222-222-2-2-2-2222-2-2-22-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ412-2222-2-2-2-12-2-2-222-2211-1-1-1112-22222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ422-2222-2-2-2-12-2-2-222-2211-1-1-1112-22222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ432-2222-2-2-2-12-2-2-222-2211-1-1-1112-2-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ442-2222-2-2-2-12-2-2-222-2211-1-1-1112-2-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ452-2222-2-2-2-1-222-222-2-211-1-1-111-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100003−3−333−3−330000000000000000
χ462-2222-2-2-2-1-222-222-2-211-1-1-111-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-10000−333−3−333−30000000000000000
χ472-2222-2-2-2-1-222-222-2-211-1-1-111-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−30000000000000000
χ482-2222-2-2-2-1-222-222-2-211-1-1-111-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−330000000000000000
χ492-22-2-2-222200022-2-20-222-2-2-2200002i−2i00−2i2i000000-22002-200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000−i2i2i2−i22−2−22
χ502-22-2-2-222200022-2-20-222-2-2-2200002i−2i00−2i2i000000-22002-200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000i2−i2−i2i2−222−2
χ512-22-2-2-222200022-2-20-222-2-2-220000−2i2i002i−2i000000-22002-20000−2i−2i2i2i00002i2i−2i−2i00000000000000000000−i2i2i2−i2−222−2
χ522-22-2-2-222200022-2-20-222-2-2-220000−2i2i002i−2i000000-22002-20000−2i−2i2i2i00002i2i−2i−2i00000000000000000000i2−i2−i2i22−2−22
χ5344444444-2444-4-4-4-44-2-2-2-2-2-2-2-4-400000000-2-222-2-222222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022-2-22222-2-22200000000000000000000000000000000000000000000
χ55444-4-44-4-440004-44-404-44-4-44-40000000000000000-4400-4400000000000000000000000000000000000000000000
χ56444-4-44-4-4-20004-44-40-22-222-2200000000000000002-2002-22323−23−2300002323−23−2300000000000000000000000000000000
χ57444-4-44-4-4-20004-44-40-22-222-2200000000000000002-2002-2−23−2323230000−23−23232300000000000000000000000000000000
χ58444-4-44-4-4-2000-44-440-22-222-2200004i−4i004i−4i000000-2200-220000−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000000000
χ59444-4-44-4-4-2000-44-440-22-222-220000−4i4i00−4i4i000000-2200-2200002i2i−2i−2i00002i2i−2i−2i0000000000000000000000000000
χ6044-44-4-44-440000000044-44-4-4-40022−220022−220000000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ6144-44-4-44-440000000044-44-4-4-400−222200−222200000000000000−2222−22220000−2222−222200000000000000000000000000000000
χ6244-44-4-44-4-200000000-2-22-22220022−220022−220000−2i32i30000−2i32i300−22−22i6−i6i6−i6−22−22i6−i6i6−i60000000000000000000000000000
χ6344-44-4-44-4-200000000-2-22-22220022−220022−2200002i3−2i300002i3−2i300−22−22−i6i6−i6i6−22−22−i6i6−i6i60000000000000000000000000000
χ6444-44-4-44-4-200000000-2-22-222200−222200−22220000−2i32i30000−2i32i3002−22−2−i6i6−i6i62−22−2−i6i6−i6i60000000000000000000000000000
χ6544-44-4-44-4-200000000-2-22-222200−222200−222200002i3−2i300002i3−2i3002−22−2i6−i6i6−i62−22−2i6−i6i6−i60000000000000000000000000000
χ6644-4-44-4-44444-40000-44-4-4-44-4400000000004-4004-400000000000000000000000000000000000000000000000000
χ6744-4-44-4-444-4-44000044-4-4-44-440000000000-4400-4400000000000000000000000000000000000000000000000000
χ6844-4-44-4-44-244-40000-4-2222-22-20000000000-2200-220000006−6−666−6−666−6−666−6−660000000000000000000000000000
χ6944-4-44-4-44-244-40000-4-2222-22-20000000000-2200-22000000−666−6−666−6−666−6−666−60000000000000000000000000000
χ7044-4-44-4-44-2-4-4400004-2222-22-200000000002-2002-20000006−6−66−666−66−6−66−666−60000000000000000000000000000
χ7144-4-44-4-44-2-4-4400004-2222-22-200000000002-2002-2000000−666−66−6−66−666−66−6−660000000000000000000000000000
χ724-4444-4-4-4-24-4-44-4-44422-2-2-222-4400000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000
χ734-4444-4-4-4-2-4444-4-44-422-2-2-2224-40000000022-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ744-44-4-4-4444000-4-4440-444-4-4-4400000000000000004-400-4400000000000000000000000000000000000000000000
χ754-44-4-4-444-200044-4-402-2-2222-200004i−4i00−4i4i0000002-200-220000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000
χ764-44-4-4-444-200044-4-402-2-2222-20000−4i4i004i−4i0000002-200-2200002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000
χ774-44-4-4-444-2000-4-44402-2-2222-20000000000000000-22002-22323−23−230000−23−23232300000000000000000000000000000000
χ784-44-4-4-444-2000-4-44402-2-2222-20000000000000000-22002-2−23−23232300002323−23−2300000000000000000000000000000000
χ794-4-44-44-44400000000-4-4-44-4440022−2200−22220000000000000022−2222−220000−2222−222200000000000000000000000000000000
χ804-4-44-44-44400000000-4-4-44-44400−22220022−2200000000000000−2222−2222000022−2222−2200000000000000000000000000000000
χ814-4-44-44-44-200000000222-22-2-20022−2200−22220000−2i32i300002i3−2i300−22−22i6−i6i6−i62−22−2−i6i6−i6i60000000000000000000000000000
χ824-4-44-44-44-200000000222-22-2-20022−2200−222200002i3−2i30000−2i32i300−22−22−i6i6−i6i62−22−2i6−i6i6−i60000000000000000000000000000
χ834-4-44-44-44-200000000222-22-2-200−22220022−220000−2i32i300002i3−2i3002−22−2−i6i6−i6i6−22−22i6−i6i6−i60000000000000000000000000000
χ844-4-44-44-44-200000000222-22-2-200−22220022−2200002i3−2i30000−2i32i3002−22−2i6−i6i6−i6−22−22−i6i6−i6i60000000000000000000000000000
χ854-4-4-4444-444-440000-4-44-4-444-400000000004-400-4400000000000000000000000000000000000000000000000000
χ864-4-4-4444-44-44-400004-44-4-444-40000000000-44004-400000000000000000000000000000000000000000000000000
χ874-4-4-4444-4-24-440000-42-222-2-220000000000-22002-20000006−6−666−6−66−666−6−666−60000000000000000000000000000
χ884-4-4-4444-4-24-440000-42-222-2-220000000000-22002-2000000−666−6−666−66−6−666−6−660000000000000000000000000000
χ894-4-4-4444-4-2-44-4000042-222-2-2200000000002-200-220000006−6−66−666−6−666−66−6−660000000000000000000000000000
χ904-4-4-4444-4-2-44-4000042-222-2-2200000000002-200-22000000−666−66−6−666−6−66−666−60000000000000000000000000000

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