Finite Group Databasebeta

← Group #10693855

Character table — Group #10693855

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
χ91111-1-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111-1-1-1-111-1-1-111-11-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111-1-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141111-1-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151111-1-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161111-1-1-1-111-1-1-111-11-1-1111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222-2-2-2-222222222-2-20000000022-2-222-2-2-2-2-2-200000000000000000000000000002-22-2000000000000
χ18222222222222-2-2-2-222222222-2-20000000022-2-222-2-2-2-2-2-20000000000000000000000000000-22-22000000000000
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
χ312222-2-2-2-222-2-22-2-222-2-2222-2-2-220000000022-2-2-2-22222-2-200000000000000000000000000002i−2i−2i2i000000000000
χ322222-2-2-2-222-2-22-2-222-2-2222-2-2-220000000022-2-2-2-22222-2-20000000000000000000000000000−2i2i2i−2i000000000000
χ332222-2-2-2-22-2222-2-22-2-2-2222-2-22-200000000-2-2222222-2-2-2-2000000000000000000000000000000002-2-2200000000
χ342222-2-2-2-22-2222-2-22-2-2-2222-2-22-200000000-2-2222222-2-2-2-200000000000000000000000000000000-222-200000000
χ352222-2-2-2-22-222-222-2-2-2-2222-2-2-2222-2-2-2-222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ362222-2-2-2-22-222-222-2-2-2-2222-2-2-22-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ372222-2-2-2-2-12-2-2-222-2211-1-1-1112-22222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ382222-2-2-2-2-12-2-2-222-2211-1-1-1112-22222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ392222-2-2-2-2-12-2-2-222-2211-1-1-1112-2-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ402222-2-2-2-2-12-2-2-222-2211-1-1-1112-2-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ412222-2-2-2-2-1-222-222-2-211-1-1-111-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100003−3−333−3−330000000000000000
χ422222-2-2-2-2-1-222-222-2-211-1-1-111-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-10000−333−3−333−30000000000000000
χ432222-2-2-2-2-1-222-222-2-211-1-1-111-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−30000000000000000
χ442222-2-2-2-2-1-222-222-2-211-1-1-111-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−330000000000000000
χ4522-2-222-2-2200022-2-20-2-22-2-22200002-2002-20000002-2002-2000022-2-2000022-2-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ4622-2-222-2-2200022-2-20-2-22-2-22200002-2002-20000002-2002-2000022-2-2000022-2-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ4722-2-222-2-2200022-2-20-2-22-2-2220000-2200-220000002-2002-20000-2-2220000-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ4822-2-222-2-2200022-2-20-2-22-2-2220000-2200-220000002-2002-20000-2-2220000-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ4922-2-2-2-2222000-22-220222-2-2-2-200002-200-22000000-22002-2000022-2-20000-2-22200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ5022-2-2-2-2222000-22-220222-2-2-2-200002-200-22000000-22002-2000022-2-20000-2-22200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ5122-2-2-2-2222000-22-220222-2-2-2-20000-22002-2000000-22002-20000-2-222000022-2-200000000000000000000−i2i2i2−i2i2−i2−i2i2
χ5222-2-2-2-2222000-22-220222-2-2-2-20000-22002-2000000-22002-20000-2-222000022-2-200000000000000000000i2−i2−i2i2−i2i2i2−i2
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
χ554444-4-4-4-4-24-4-44-4-44422-2-2-222-4400000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4444-4-44-422-2-2-2224-40000000022-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ5744-4-444-4-44000-4-4440-4-44-4-4440000000000000000-4400-4400000000000000000000000000000000000000000000
χ5844-4-444-4-4-200044-4-4022-222-2-200004-4004-4000000-2200-220000-2-2220000-2-2220000000000000000000000000000
χ5944-4-444-4-4-200044-4-4022-222-2-20000-4400-44000000-2200-22000022-2-2000022-2-20000000000000000000000000000
χ6044-4-444-4-4-2000-4-444022-222-2-200000000000000002-2002-2−2i3−2i32i32i30000−2i3−2i32i32i300000000000000000000000000000000
χ6144-4-444-4-4-2000-4-444022-222-2-200000000000000002-2002-22i32i3−2i3−2i300002i32i3−2i3−2i300000000000000000000000000000000
χ6244-4-4-4-44440004-44-40444-4-4-4-400000000000000004-400-4400000000000000000000000000000000000000000000
χ6344-4-4-4-444-20004-44-40-2-2-222220000000000000000-22002-2−2i3−2i32i32i300002i32i3−2i3−2i300000000000000000000000000000000
χ6444-4-4-4-444-20004-44-40-2-2-222220000000000000000-22002-22i32i3−2i3−2i30000−2i3−2i32i32i300000000000000000000000000000000
χ6544-4-4-4-444-2000-44-440-2-2-2222200004-400-440000002-200-220000-2-222000022-2-20000000000000000000000000000
χ6644-4-4-4-444-2000-44-440-2-2-222220000-44004-40000002-200-22000022-2-20000-2-2220000000000000000000000000000
χ674-44-44-44-44000000004-4-44-44-400−2i22i200−2i22i200000000000000−2i22i2−2i22i20000−2i22i2−2i22i200000000000000000000000000000000
χ684-44-44-44-44000000004-4-44-44-4002i2−2i2002i2−2i2000000000000002i2−2i22i2−2i200002i2−2i22i2−2i200000000000000000000000000000000
χ694-44-44-44-4-200000000-222-22-2200−2i22i200−2i22i20000−2i32i30000−2i32i300i2−i2i2−i26−66−6i2−i2i2−i26−66−60000000000000000000000000000
χ704-44-44-44-4-200000000-222-22-2200−2i22i200−2i22i200002i3−2i300002i3−2i300i2−i2i2−i2−66−66i2−i2i2−i2−66−660000000000000000000000000000
χ714-44-44-44-4-200000000-222-22-22002i2−2i2002i2−2i20000−2i32i30000−2i32i300−i2i2−i2i2−66−66−i2i2−i2i2−66−660000000000000000000000000000
χ724-44-44-44-4-200000000-222-22-22002i2−2i2002i2−2i200002i3−2i300002i3−2i300−i2i2−i2i26−66−6−i2i2−i2i26−66−60000000000000000000000000000
χ734-44-4-44-44400000000-44-44-4-4400−2i22i2002i2−2i200000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000
χ744-44-4-44-44400000000-44-44-4-44002i2−2i200−2i22i2000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000
χ754-44-4-44-44-2000000002-22-222-200−2i22i2002i2−2i20000−2i32i300002i3−2i300i2−i2i2−i26−66−6−i2i2−i2i2−66−660000000000000000000000000000
χ764-44-4-44-44-2000000002-22-222-200−2i22i2002i2−2i200002i3−2i30000−2i32i300i2−i2i2−i2−66−66−i2i2−i2i26−66−60000000000000000000000000000
χ774-44-4-44-44-2000000002-22-222-2002i2−2i200−2i22i20000−2i32i300002i3−2i300−i2i2−i2i2−66−66i2−i2i2−i26−66−60000000000000000000000000000
χ784-44-4-44-44-2000000002-22-222-2002i2−2i200−2i22i200002i3−2i30000−2i32i300−i2i2−i2i26−66−6i2−i2i2−i2−66−660000000000000000000000000000
χ794-4-444-4-44444-40000-4-44-4-444-400000000004-4004-400000000000000000000000000000000000000000000000000
χ804-4-444-4-444-4-4400004-44-4-444-40000000000-4400-4400000000000000000000000000000000000000000000000000
χ814-4-444-4-44-244-40000-42-222-2-220000000000-2200-220000006−6−666−6−666−6−666−6−660000000000000000000000000000
χ824-4-444-4-44-244-40000-42-222-2-220000000000-2200-22000000−666−6−666−6−666−6−666−60000000000000000000000000000
χ834-4-444-4-44-2-4-44000042-222-2-2200000000002-2002-20000006−6−66−666−66−6−66−666−60000000000000000000000000000
χ844-4-444-4-44-2-4-44000042-222-2-2200000000002-2002-2000000−666−66−6−66−666−66−6−660000000000000000000000000000
χ854-4-44-444-444-440000-44-4-4-44-4400000000004-400-4400000000000000000000000000000000000000000000000000
χ864-4-44-444-44-44-4000044-4-4-44-440000000000-44004-400000000000000000000000000000000000000000000000000
χ874-4-44-444-4-24-440000-4-2222-22-20000000000-22002-20000006−6−666−6−66−666−6−666−60000000000000000000000000000
χ884-4-44-444-4-24-440000-4-2222-22-20000000000-22002-2000000−666−6−666−66−6−666−6−660000000000000000000000000000
χ894-4-44-444-4-2-44-400004-2222-22-200000000002-200-220000006−6−66−666−6−666−66−6−660000000000000000000000000000
χ904-4-44-444-4-2-44-400004-2222-22-200000000002-200-22000000−666−66−6−666−6−66−666−60000000000000000000000000000

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