Finite Group Databasebeta

← Group #10695331

Character table — Group #10695331

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666444444444412121212121212121212121212121212121212121212121212121212444412121212121212128888888888888888
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
χ9111111111-1-1-1-1-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111-1-1-1-1-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111-1-1-1-1-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111-1-1-1-1-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111-1-1-1-1-1-1-1-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111-1-1-1-1-1-1-1-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111-1-1-1-1-1-1-1-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111-1-1-1-1-1-1-1-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222222222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ19222222222-2-2-22222-22222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ20222222222-2-2-22222-22222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ2522222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-222-2-2-2-2221111-1-1-1-11111-1-1-1-111111111-1-1-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2622222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-222-2-2-2-2221111-1-1-1-11111-1-1-1-111111111-1-1-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2722222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2822222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2922222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1111111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3022222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1111111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3122222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ3222222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-222-1-1-1-1111111111111-1-1-1-11111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-222-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ372222-2-2-2-2200022-2-20222-2-2-2-2002-22-200000000000022-2-222-2-222-2-200000000000000000000000000002−22−22−22−2
χ382222-2-2-2-2200022-2-20222-2-2-2-2002-22-200000000000022-2-222-2-222-2-20000000000000000000000000000−22−22−22−22
χ392222-2-2-2-2200022-2-20222-2-2-2-200-22-2200000000000022-2-2-2-222-2-22200000000000000000000000000002−22−2−22−22
χ402222-2-2-2-2200022-2-20222-2-2-2-200-22-2200000000000022-2-2-2-222-2-2220000000000000000000000000000−22−222−22−2
χ412222-2-2-2-22000-2-2220222-2-2-2-2002-2-22000000000000-2-22222-2-2-2-2220000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ422222-2-2-2-22000-2-2220222-2-2-2-2002-2-22000000000000-2-22222-2-2-2-2220000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ432222-2-2-2-22000-2-2220222-2-2-2-200-222-2000000000000-2-222-2-22222-2-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ442222-2-2-2-22000-2-2220222-2-2-2-200-222-2000000000000-2-222-2-22222-2-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ4522-2-222-2-2222-22-22-2-22-2-222-2-22-20000000022-2-222-2-22-22-2000000000000000000000000000000002-22-200000000
χ4622-2-222-2-2222-22-22-2-22-2-222-2-22-20000000022-2-222-2-22-22-200000000000000000000000000000000-22-2200000000
χ4722-2-222-2-2222-2-22-22-22-2-222-2-2-2200000000-2-22222-2-2-22-2200000000000000000000000000002-22-2000000000000
χ4822-2-222-2-2222-2-22-22-22-2-222-2-2-2200000000-2-22222-2-2-22-220000000000000000000000000000-22-22000000000000
χ4922-2-222-2-22-2-222-22-222-2-222-2-2-2200000000-2-222-2-2222-22-200000000000000000000000000002i−2i−2i2i000000000000
χ5022-2-222-2-22-2-222-22-222-2-222-2-2-2200000000-2-222-2-2222-22-20000000000000000000000000000−2i2i2i−2i000000000000
χ5122-2-222-2-22-2-22-22-2222-2-222-2-22-20000000022-2-2-2-222-22-22000000000000000000000000000000002i−2i−2i2i00000000
χ5222-2-222-2-22-2-22-22-2222-2-222-2-22-20000000022-2-2-2-222-22-2200000000000000000000000000000000−2i2i2i−2i00000000
χ534444-4-4-4-4-200044-4-40-2-2-22222004-44-4000000000000-2-222-2-222-2-222000000000000000000000000000000000000
χ544444-4-4-4-4-200044-4-40-2-2-2222200-44-44000000000000-2-22222-2-222-2-2000000000000000000000000000000000000
χ554444-4-4-4-4-2000-4-4440-2-2-22222004-4-4400000000000022-2-2-2-22222-2-2000000000000000000000000000000000000
χ564444-4-4-4-4-2000-4-4440-2-2-2222200-444-400000000000022-2-222-2-2-2-222000000000000000000000000000000000000
χ5744-4-444-4-4-244-44-44-4-4-222-2-2224-400000000-2-222-2-222-22-2200000000000000000000000000000000000000000000
χ5844-4-444-4-4-244-4-44-44-4-222-2-222-440000000022-2-2-2-2222-22-200000000000000000000000000000000000000000000
χ5944-4-444-4-4-2-4-444-44-44-222-2-222-440000000022-2-222-2-2-22-2200000000000000000000000000000000000000000000
χ6044-4-444-4-4-2-4-44-44-444-222-2-2224-400000000-2-22222-2-22-22-200000000000000000000000000000000000000000000
χ6144-4-4-4-44440004-4-4404-4-4-4-4440000000000000000004-4-4400000000000000000000000000000000000000000000
χ6244-4-4-4-4444000-444-404-4-4-4-444000000000000000000-444-400000000000000000000000000000000000000000000
χ6344-4-4-4-444-20004-4-440-22222-2-2000000000000000000-222-200000000−2i3−2i32i32i3−2i3−2i32i32i30000000000000000000000000000
χ6444-4-4-4-444-20004-4-440-22222-2-2000000000000000000-222-2000000002i32i3−2i3−2i32i32i3−2i3−2i30000000000000000000000000000
χ6544-4-4-4-444-2000-444-40-22222-2-20000000000000000002-2-2200000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000
χ6644-4-4-4-444-2000-444-40-22222-2-20000000000000000002-2-22000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000
χ674-44-44-44-4400000000-44-44-44-4000000004i−4i0000000000000000000000004i−4i4i−4i0000000000000000000000000000
χ684-44-44-44-4400000000-44-44-44-400000000−4i4i000000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ694-44-44-44-4-2000000002-22-22-22000000004i−4i−2i32i3−2i32i300000000000023−2323−230000−2i2i−2i2i0000000000000000000000000000
χ704-44-44-44-4-2000000002-22-22-22000000004i−4i2i3−2i32i3−2i3000000000000−2323−23230000−2i2i−2i2i0000000000000000000000000000
χ714-44-44-44-4-2000000002-22-22-2200000000−4i4i−2i32i3−2i32i3000000000000−2323−232300002i−2i2i−2i0000000000000000000000000000
χ724-44-44-44-4-2000000002-22-22-2200000000−4i4i2i3−2i32i3−2i300000000000023−2323−2300002i−2i2i−2i0000000000000000000000000000
χ734-44-4-44-4444-440000-4-44-4-44-44000000000000004-44-4000000000000000000000000000000000000000000000000
χ744-44-4-44-444-44-400004-44-4-44-4400000000000000-44-44000000000000000000000000000000000000000000000000
χ754-44-4-44-44-24-440000-42-222-22-200000000000000-22-220000000023−23−232323−2323−2300000000000000000000000000000000
χ764-44-4-44-44-24-440000-42-222-22-200000000000000-22-2200000000−232323−23−2323−232300000000000000000000000000000000
χ774-44-4-44-44-2-44-4000042-222-22-2000000000000002-22-20000000023−23−2323−2323−232300000000000000000000000000000000
χ784-44-4-44-44-2-44-4000042-222-22-2000000000000002-22-200000000−232323−2323−2323−2300000000000000000000000000000000
χ794-4-444-4-44400000000-4-444-4-440000004i−4i00000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ804-4-444-4-44400000000-4-444-4-44000000−4i4i0000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ814-4-444-4-44-20000000022-2-222-20000004i−4i00−2i32i32i3−2i30000000023−2323−230000−2i2i2i−2i00000000000000000000000000000000
χ824-4-444-4-44-20000000022-2-222-20000004i−4i002i3−2i3−2i32i300000000−2323−23230000−2i2i2i−2i00000000000000000000000000000000
χ834-4-444-4-44-20000000022-2-222-2000000−4i4i00−2i32i32i3−2i300000000−2323−232300002i−2i−2i2i00000000000000000000000000000000
χ844-4-444-4-44-20000000022-2-222-2000000−4i4i002i3−2i3−2i32i30000000023−2323−2300002i−2i−2i2i00000000000000000000000000000000
χ854-4-44-444-444-4-400004-4-44-444-4000000000000004-4-44000000000000000000000000000000000000000000000000
χ864-4-44-444-44-4440000-4-4-44-444-400000000000000-444-4000000000000000000000000000000000000000000000000
χ874-4-44-444-4-24-4-40000422-22-2-2200000000000000-222-2000023−23−232300000000−232323−230000000000000000000000000000
χ884-4-44-444-4-24-4-40000422-22-2-2200000000000000-222-20000−232323−230000000023−23−23230000000000000000000000000000
χ894-4-44-444-4-2-4440000-422-22-2-22000000000000002-2-22000023−23−23230000000023−23−23230000000000000000000000000000
χ904-4-44-444-4-2-4440000-422-22-2-22000000000000002-2-220000−232323−2300000000−232323−230000000000000000000000000000

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