Finite Group Databasebeta

← Group #10694523

Character table — Group #10694523

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
χ91-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121-1-1111-1-1111-1-111-1-1-1-1-1-11111-11111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131-1-1111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141-1-1111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151-1-1111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161-1-1111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222222222-2-200000000-2-2-2-22222-2-2-2-200000000000000000000000000002-22-2000000000000
χ18222222222222-2-2-2-222222222-2-200000000-2-2-2-22222-2-2-2-20000000000000000000000000000-22-22000000000000
χ19222222222-2-2-22222-22222222-2-222-2-222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-2-2-22222-22222222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-2000000000000000000000000000000002i−2i2i−2i00000000
χ22222222222-2-2-2-2-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-200000000000000000000000000000000−2i2i−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
χ2722222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-222-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-222-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ31222-22-2-2-22000-22-22022-2-2-22-200002i−2i002i−2i000000002-22-200002i2i−2i−2i00002i2i−2i−2i00000000000000000000−i2i2−i2i22−22−2
χ32222-22-2-2-22000-22-22022-2-2-22-200002i−2i002i−2i000000002-22-200002i2i−2i−2i00002i2i−2i−2i00000000000000000000i2−i2i2−i2−22−22
χ33222-22-2-2-22000-22-22022-2-2-22-20000−2i2i00−2i2i000000002-22-20000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000−i2i2−i2i2−22−22
χ34222-22-2-2-22000-22-22022-2-2-22-20000−2i2i00−2i2i000000002-22-20000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000i2−i2i2−i22−22−2
χ352-2-2222-2-2222-22-2-22-2-2-2-2-2222-2200000000-2-22222-2-222-2-200000000000000000000000000002i−2i−2i2i000000000000
χ362-2-2222-2-2222-22-2-22-2-2-2-2-2222-2200000000-2-22222-2-222-2-20000000000000000000000000000−2i2i2i−2i000000000000
χ372-2-2222-2-22-2-222-2-222-2-2-2-22222-20000000022-2-2-2-22222-2-2000000000000000000000000000000002-2-2200000000
χ382-2-2222-2-22-2-222-2-222-2-2-2-22222-20000000022-2-2-2-22222-2-200000000000000000000000000000000-222-200000000
χ392-2-2222-2-22-2-22-222-22-2-2-2-2222-2222-2-2-2-222-2-222-2-222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ402-2-2222-2-22-2-22-222-22-2-2-2-2222-22-2-22222-2-2-2-222-2-222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ412-2-2222-2-2-122-2-222-2-21111-1-1-12-22222-2-2-2-2-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000
χ422-2-2222-2-2-122-2-222-2-21111-1-1-12-22222-2-2-2-2-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-10000000000000000
χ432-2-2222-2-2-122-2-222-2-21111-1-1-12-2-2-2-2-22222-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-10000000000000000
χ442-2-2222-2-2-122-2-222-2-21111-1-1-12-2-2-2-2-22222-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-1110000000000000000
χ452-2-2222-2-2-1-2-22-222-221111-1-1-1-2222-2-2-2-22211-1-111-1-111-1-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ462-2-2222-2-2-1-2-22-222-221111-1-1-1-2222-2-2-2-22211-1-111-1-111-1-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ472-2-2222-2-2-1-2-22-222-221111-1-1-1-22-2-22222-2-211-1-111-1-111-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ482-2-2222-2-2-1-2-22-222-221111-1-1-1-22-2-22222-2-211-1-111-1-111-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ492-2-2-22-222200022-2-20-2-222-22-200002i−2i00−2i2i00000000-222-200002i2i−2i−2i0000−2i−2i2i2i000000000000000000002−2−22i2−i2−i2i2
χ502-2-2-22-222200022-2-20-2-222-22-200002i−2i00−2i2i00000000-222-200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000−222−2−i2i2i2−i2
χ512-2-2-22-222200022-2-20-2-222-22-20000−2i2i002i−2i00000000-222-20000−2i−2i2i2i00002i2i−2i−2i000000000000000000002−2−22−i2i2i2−i2
χ522-2-2-22-222200022-2-20-2-222-22-20000−2i2i002i−2i00000000-222-20000−2i−2i2i2i00002i2i−2i−2i00000000000000000000−222−2i2−i2−i2i2
χ5344444444-2444-4-4-4-44-2-2-2-2-2-2-2-4-4000000002222-2-2-2-2222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ55444-44-4-4-440004-44-4044-4-4-44-4000000000000000000-44-4400000000000000000000000000000000000000000000
χ56444-44-4-4-4-20004-44-40-2-2222-220000000000000000002-22-22323−23−2300002323−23−2300000000000000000000000000000000
χ57444-44-4-4-4-20004-44-40-2-2222-220000000000000000002-22-2−23−2323230000−23−23232300000000000000000000000000000000
χ58444-44-4-4-4-2000-44-440-2-2222-2200004i−4i004i−4i00000000-22-220000−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000000000
χ59444-44-4-4-4-2000-44-440-2-2222-220000−4i4i00−4i4i00000000-22-2200002i2i−2i−2i00002i2i−2i−2i0000000000000000000000000000
χ6044-44-4-44-44000000004-44-44-4-40022−220022−220000000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ6144-44-4-44-44000000004-44-44-4-400−222200−222200000000000000−2222−22220000−2222−222200000000000000000000000000000000
χ6244-44-4-44-4-200000000-22-22-2220022−220022−2200−2i32i3−2i32i300000000−22−22i6−i6i6−i6−22−22i6−i6i6−i60000000000000000000000000000
χ6344-44-4-44-4-200000000-22-22-2220022−220022−22002i3−2i32i3−2i300000000−22−22−i6i6−i6i6−22−22−i6i6−i6i60000000000000000000000000000
χ6444-44-4-44-4-200000000-22-22-22200−222200−222200−2i32i3−2i32i3000000002−22−2−i6i6−i6i62−22−2−i6i6−i6i60000000000000000000000000000
χ6544-44-4-44-4-200000000-22-22-22200−222200−2222002i3−2i32i3−2i3000000002−22−2i6−i6i6−i62−22−2i6−i6i6−i60000000000000000000000000000
χ6644-4-4-44-4444-440000-44-4-44-4-44000000000000004-44-4000000000000000000000000000000000000000000000000
χ6744-4-4-44-444-44-4000044-4-44-4-4400000000000000-44-44000000000000000000000000000000000000000000000000
χ6844-4-4-44-44-24-440000-4-222-222-200000000000000-22-2200006−6−666−6−666−6−666−6−660000000000000000000000000000
χ6944-4-4-44-44-24-440000-4-222-222-200000000000000-22-220000−666−6−666−6−666−6−666−60000000000000000000000000000
χ7044-4-4-44-44-2-44-400004-222-222-2000000000000002-22-200006−6−66−666−66−6−66−666−60000000000000000000000000000
χ7144-4-4-44-44-2-44-400004-222-222-2000000000000002-22-20000−666−66−6−66−666−66−6−660000000000000000000000000000
χ724-444-4-4-44400000000-44-444-4-40022−2200−22220000000000000022−2222−220000−2222−222200000000000000000000000000000000
χ734-444-4-4-44400000000-44-444-4-400−22220022−2200000000000000−2222−2222000022−2222−2200000000000000000000000000000000
χ744-444-4-4-44-2000000002-22-2-2220022−2200−222200−2i32i32i3−2i300000000−22−22i6−i6i6−i62−22−2−i6i6−i6i60000000000000000000000000000
χ754-444-4-4-44-2000000002-22-2-2220022−2200−2222002i3−2i3−2i32i300000000−22−22−i6i6−i6i62−22−2i6−i6i6−i60000000000000000000000000000
χ764-444-4-4-44-2000000002-22-2-22200−22220022−2200−2i32i32i3−2i3000000002−22−2−i6i6−i6i6−22−22i6−i6i6−i60000000000000000000000000000
χ774-444-4-4-44-2000000002-22-2-22200−22220022−22002i3−2i3−2i32i3000000002−22−2i6−i6i6−i6−22−22−i6i6−i6i60000000000000000000000000000
χ784-44-4-444-444-4-400004-444-4-4-44000000000000004-4-44000000000000000000000000000000000000000000000000
χ794-44-4-444-44-4440000-4-444-4-4-4400000000000000-444-4000000000000000000000000000000000000000000000000
χ804-44-4-444-4-24-4-4000042-2-2222-200000000000000-222-200006−6−666−6−66−666−6−666−60000000000000000000000000000
χ814-44-4-444-4-24-4-4000042-2-2222-200000000000000-222-20000−666−6−666−66−6−666−6−660000000000000000000000000000
χ824-44-4-444-4-2-4440000-42-2-2222-2000000000000002-2-2200006−6−66−666−6−666−66−6−660000000000000000000000000000
χ834-44-4-444-4-2-4440000-42-2-2222-2000000000000002-2-220000−666−66−6−666−6−66−666−60000000000000000000000000000
χ844-4-4444-4-4-244-44-4-44-42222-2-2-2-440000000022-2-2-2-222-2-22200000000000000000000000000000000000000000000
χ854-4-4444-4-4-2-4-444-4-4442222-2-2-24-400000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000
χ864-4-4-44-4444000-4-4440-4-444-44-40000000000000000004-4-4400000000000000000000000000000000000000000000
χ874-4-4-44-444-200044-4-4022-2-22-2200004i−4i00−4i4i000000002-2-220000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000
χ884-4-4-44-444-200044-4-4022-2-22-220000−4i4i004i−4i000000002-2-2200002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000
χ894-4-4-44-444-2000-4-444022-2-22-22000000000000000000-222-22323−23−230000−23−23232300000000000000000000000000000000
χ904-4-4-44-444-2000-4-444022-2-22-22000000000000000000-222-2−23−23232300002323−23−2300000000000000000000000000000000

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