Finite Group Databasebeta

← Group #10690868

Character table — Group #10690868

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222222344444444666666622444444446666121212121212121212121212121212121212121212121212444412121212121212128888888888888888
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
χ5111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-222-2-222222222222-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-222-2-22222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222-2-222-2-222222222222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ20222222222-2-222-2-2222222222-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
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
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-1111122-2-2-1-1-1-111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-11111-2-2221111-1-1-1-10000000000000000
χ2522222222-122-2-222-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111-1-1-1-11111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2622222222-122-2-222-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111-1-1-1-11111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2722222222-122-2-222-2-2-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2822222222-122-2-222-2-2-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2922222222-1-2-222-2-222-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3022222222-1-2-222-2-222-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3122222222-1-2-222-2-222-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ3222222222-1-2-222-2-222-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-12-22-2-1-111-1-1110000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-22-2211-1-111-1-10000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222222-2-2111111111111-1-1-1-1-1-1-1-1-1-1-1-111112-2-22-1-11111-1-10000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222222-2-2111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-222-211-1-1-1-1110000000000000000
χ3722-2-22-22-22002-2002-22-2-22-22-2002i−2i00002i−2i0000000022-2-22i2i−2i−2i000000002i2i−2i−2i0000000000002−22−2−i2i2−i2i200000000
χ3822-2-22-22-22002-2002-22-2-22-22-2002i−2i00002i−2i0000000022-2-22i2i−2i−2i000000002i2i−2i−2i000000000000−22−22i2−i2i2−i200000000
χ3922-2-22-22-22002-2002-22-2-22-22-200−2i2i0000−2i2i0000000022-2-2−2i−2i2i2i00000000−2i−2i2i2i0000000000002−22−2i2−i2i2−i200000000
χ4022-2-22-22-22002-2002-22-2-22-22-200−2i2i0000−2i2i0000000022-2-2−2i−2i2i2i00000000−2i−2i2i2i000000000000−22−22−i2i2−i2i200000000
χ4122-2-22-22-2200-2200-222-2-22-22-2002i−2i0000−2i2i00000000-2-2222i2i−2i−2i00000000−2i−2i2i2i000000000000−i2i2i2−i22−2−2200000000
χ4222-2-22-22-2200-2200-222-2-22-22-2002i−2i0000−2i2i00000000-2-2222i2i−2i−2i00000000−2i−2i2i2i000000000000i2−i2−i2i2−222−200000000
χ4322-2-22-22-2200-2200-222-2-22-22-200−2i2i00002i−2i00000000-2-222−2i−2i2i2i000000002i2i−2i−2i000000000000−i2i2i2−i2−222−200000000
χ4422-2-22-22-2200-2200-222-2-22-22-200−2i2i00002i−2i00000000-2-222−2i−2i2i2i000000002i2i−2i−2i000000000000i2−i2−i2i22−2−2200000000
χ452-2-2-222-2222-2222-2-2-2-2-2-222-220000002-200000022-2-22-22-20000000022-2-20000000000000000000000002i−2i2i−2i0000
χ462-2-2-222-2222-2222-2-2-2-2-2-222-220000002-200000022-2-22-22-20000000022-2-2000000000000000000000000−2i2i−2i2i0000
χ472-2-2-222-2222-2-2-22-222-2-2-222-22000000-2200000022-2-2-22-2200000000-2-22200000000000000000000000000002-22-2
χ482-2-2-222-2222-2-2-22-222-2-2-222-22000000-2200000022-2-2-22-2200000000-2-2220000000000000000000000000000-22-22
χ492-2-2-222-222-2222-22-2-2-2-2-222-22000000-22000000-2-2222-22-200000000-2-22200000000000000000000000000002i−2i−2i2i
χ502-2-2-222-222-2222-22-2-2-2-2-222-22000000-22000000-2-2222-22-200000000-2-2220000000000000000000000000000−2i2i2i−2i
χ512-2-2-222-222-22-2-2-2222-2-2-222-220000002-2000000-2-222-22-220000000022-2-20000000000000000000000002-2-220000
χ522-2-2-222-222-22-2-2-2222-2-2-222-220000002-2000000-2-222-22-220000000022-2-2000000000000000000000000-222-20000
χ53444-4-44-4-444-400-440044-4-44-4-4000000000000004-44-4000000000000000000000000000000000000000000000000
χ54444-4-44-4-44-44004-40044-4-44-4-400000000000000-44-44000000000000000000000000000000000000000000000000
χ55444-4-44-4-4-24-400-4400-2-222-2220000000000−2i3−2i32i32i3-22-220000−2i32i3−2i32i30000000000000000000000000000000000000000
χ56444-4-44-4-4-24-400-4400-2-222-22200000000002i32i3−2i3−2i3-22-2200002i3−2i32i3−2i30000000000000000000000000000000000000000
χ57444-4-44-4-4-2-44004-400-2-222-2220000000000−2i3−2i32i32i32-22-200002i3−2i32i3−2i30000000000000000000000000000000000000000
χ58444-4-44-4-4-2-44004-400-2-222-22200000000002i32i3−2i3−2i32-22-20000−2i32i3−2i32i30000000000000000000000000000000000000000
χ5944-44-4-4-444000000004-44-4-4-4400004i−4i000000000000000000004i4i−4i−4i000000000000000000000000000000000000
χ6044-44-4-4-444000000004-44-4-4-440000−4i4i00000000000000000000−4i−4i4i4i000000000000000000000000000000000000
χ6144-44-4-4-44-200000000-22-2222-200004i−4i000000000000000023−23−2323−2i−2i2i2i−2i32i3−2i32i300000000000000000000000000000000
χ6244-44-4-4-44-200000000-22-2222-200004i−4i0000000000000000−232323−23−2i−2i2i2i2i3−2i32i3−2i300000000000000000000000000000000
χ6344-44-4-4-44-200000000-22-2222-20000−4i4i000000000000000023−23−23232i2i−2i−2i2i3−2i32i3−2i300000000000000000000000000000000
χ6444-44-4-4-44-200000000-22-2222-20000−4i4i0000000000000000−232323−232i2i−2i−2i−2i32i3−2i32i300000000000000000000000000000000
χ6544-4-44-44-4-2004-4004-4-222-22-22004i−4i00004i−4i00000000-2-222−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000000000
χ6644-4-44-44-4-2004-4004-4-222-22-2200−4i4i0000−4i4i00000000-2-2222i2i−2i−2i000000002i2i−2i−2i0000000000000000000000000000
χ6744-4-44-44-4-200-4400-44-222-22-22004i−4i0000−4i4i0000000022-2-2−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000000000
χ6844-4-44-44-4-200-4400-44-222-22-2200−4i4i00004i−4i0000000022-2-22i2i−2i−2i00000000−2i−2i2i2i0000000000000000000000000000
χ694-4444-4-4-44004-400-44-4444-4-4-40000000000000000004-4-4400000000000000000000000000000000000000000000
χ704-4444-4-4-4400-44004-4-4444-4-4-4000000000000000000-444-400000000000000000000000000000000000000000000
χ714-4444-4-4-4-2004-400-442-2-2-22220000000000−2i32i3−2i32i30000-222-20000−2i32i3−2i32i3000000000000000000000000000000000000
χ724-4444-4-4-4-2004-400-442-2-2-222200000000002i3−2i32i3−2i30000-222-200002i3−2i32i3−2i3000000000000000000000000000000000000
χ734-4444-4-4-4-200-44004-42-2-2-22220000000000−2i32i3−2i32i300002-2-2200002i3−2i32i3−2i3000000000000000000000000000000000000
χ744-4444-4-4-4-200-44004-42-2-2-222200000000002i3−2i32i3−2i300002-2-220000−2i32i3−2i32i3000000000000000000000000000000000000
χ754-44-4-4-444400000000-44-4-4-4444-4000000004-4-440000000000000000000000000000000000000000000000000000
χ764-44-4-4-444400000000-44-4-4-444-4400000000-444-40000000000000000000000000000000000000000000000000000
χ774-44-4-4-444-2000000002-2222-2-24-400000000-222-20000000000000000−2i32i32i3−2i3−2i32i3−2i32i30000000000000000000000000000
χ784-44-4-4-444-2000000002-2222-2-24-400000000-222-200000000000000002i3−2i3−2i32i32i3−2i32i3−2i30000000000000000000000000000
χ794-44-4-4-444-2000000002-2222-2-2-44000000002-2-220000000000000000−2i32i32i3−2i32i3−2i32i3−2i30000000000000000000000000000
χ804-44-4-4-444-2000000002-2222-2-2-44000000002-2-2200000000000000002i3−2i3−2i32i3−2i32i3−2i32i30000000000000000000000000000
χ814-4-44-444-444400-4-400-4-44-444-4000000000000004-4-44000000000000000000000000000000000000000000000000
χ824-4-44-444-44-4-4004400-4-44-444-400000000000000-444-4000000000000000000000000000000000000000000000000
χ834-4-44-444-4-24400-4-40022-22-2-2200000000000000-222-20000000023−23−23230000−232323−230000000000000000000000000000
χ844-4-44-444-4-24400-4-40022-22-2-2200000000000000-222-200000000−232323−23000023−23−23230000000000000000000000000000
χ854-4-44-444-4-2-4-400440022-22-2-22000000000000002-2-220000000023−23−2323000023−23−23230000000000000000000000000000
χ864-4-44-444-4-2-4-400440022-22-2-22000000000000002-2-2200000000−232323−230000−232323−230000000000000000000000000000
χ874-4-4-444-44-24-4444-4-4-4222-2-22-20000004-4000000-2-222-22-2200000000-2-22200000000000000000000000000000000
χ884-4-4-444-44-24-4-4-44-444222-2-22-2000000-44000000-2-2222-22-20000000022-2-200000000000000000000000000000000
χ894-4-4-444-44-2-4444-44-4-4222-2-22-2000000-4400000022-2-2-22-220000000022-2-200000000000000000000000000000000
χ904-4-4-444-44-2-44-4-4-4444222-2-22-20000004-400000022-2-22-22-200000000-2-22200000000000000000000000000000000

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