Finite Group Databasebeta

← Group #10690803

Character table — Group #10690803

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666224444444466661212121212121212121212121212121212121212121212122444661212121212128888888888888888
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
χ5111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ14111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ15111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ16111111111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-2-2-22222222222222-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222-2-22222-2-2222222222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ20222222222-2-22222-2-22222222-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
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
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-111112-2-22-1-11111-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-11111-222-211-1-1-1-1110000000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111-1-1-1-11111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111-1-1-1-11111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-122-2-2-1-1-1-111110000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-2221111-1-1-1-10000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222222-2-2111111111111-1-1-1-1-1-1-1-1-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222222-2-2111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ3722-222-2-2-222i−2i00002i−2i2-222-2-2-22-22i−2i00000022-2-22i2i−2i−2i00002i2i−2i−2i0000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ3822-222-2-2-222i−2i00002i−2i2-222-2-2-22-22i−2i00000022-2-22i2i−2i−2i00002i2i−2i−2i000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ3922-222-2-2-222i−2i00002i−2i2-222-2-2-2-22−2i2i000000-2-2222i2i−2i−2i0000−2i−2i2i2i0000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ4022-222-2-2-222i−2i00002i−2i2-222-2-2-2-22−2i2i000000-2-2222i2i−2i−2i0000−2i−2i2i2i000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ4122-222-2-2-22−2i2i0000−2i2i2-222-2-2-22-2−2i2i00000022-2-2−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ4222-222-2-2-22−2i2i0000−2i2i2-222-2-2-22-2−2i2i00000022-2-2−2i−2i2i2i0000−2i−2i2i2i000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ4322-222-2-2-22−2i2i0000−2i2i2-222-2-2-2-222i−2i000000-2-222−2i−2i2i2i00002i2i−2i−2i0000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ4422-222-2-2-22−2i2i0000−2i2i2-222-2-2-2-222i−2i000000-2-222−2i−2i2i2i00002i2i−2i−2i000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ452-2-22-22-2222222-2-2-2-2-2-22-22-220000002-20000002-22-222-2-20000000022-2-200000000000000000000000000002i−2i2i−2i
χ462-2-22-22-2222222-2-2-2-2-2-22-22-220000002-20000002-22-222-2-20000000022-2-20000000000000000000000000000−2i2i−2i2i
χ472-2-22-22-22222-2-222-2-2-2-22-22-22000000-220000002-22-2-2-22200000000-2-2220000000000000000000000002i−2i2i−2i0000
χ482-2-22-22-22222-2-222-2-2-2-22-22-22000000-220000002-22-2-2-22200000000-2-222000000000000000000000000−2i2i−2i2i0000
χ492-2-22-22-222-2-222-2-222-2-22-22-22000000-22000000-22-2222-2-200000000-2-2220000000000000000000000002-2-220000
χ502-2-22-22-222-2-222-2-222-2-22-22-22000000-22000000-22-2222-2-200000000-2-222000000000000000000000000-222-20000
χ512-2-22-22-222-2-2-2-22222-2-22-22-220000002-2000000-22-22-2-2220000000022-2-200000000000000000000000000002-2-22
χ522-2-22-22-222-2-2-2-22222-2-22-22-220000002-2000000-22-22-2-2220000000022-2-20000000000000000000000000000-222-2
χ53444-4-4-4-4440000000044-4-4-4-4400004i−4i000000000000000000004i4i−4i−4i000000000000000000000000000000000000
χ54444-4-4-4-4440000000044-4-4-4-440000−4i4i00000000000000000000−4i−4i4i4i000000000000000000000000000000000000
χ55444-4-4-4-44-200000000-2-22222-200004i−4i000000000000000023−2323−23−2i−2i2i2i−2i32i3−2i32i300000000000000000000000000000000
χ56444-4-4-4-44-200000000-2-22222-200004i−4i0000000000000000−2323−2323−2i−2i2i2i2i3−2i32i3−2i300000000000000000000000000000000
χ57444-4-4-4-44-200000000-2-22222-20000−4i4i000000000000000023−2323−232i2i−2i−2i2i3−2i32i3−2i300000000000000000000000000000000
χ58444-4-4-4-44-200000000-2-22222-20000−4i4i0000000000000000−2323−23232i2i−2i−2i−2i32i3−2i32i300000000000000000000000000000000
χ5944-444-4-4-4-24i−4i00004i−4i-22-2-22224-44i−4i000000-2-222−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ6044-444-4-4-4-24i−4i00004i−4i-22-2-2222-44−4i4i00000022-2-2−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000000000000000
χ6144-444-4-4-4-2−4i4i0000−4i4i-22-2-22224-4−4i4i000000-2-2222i2i−2i−2i00002i2i−2i−2i0000000000000000000000000000000000000000
χ6244-444-4-4-4-2−4i4i0000−4i4i-22-2-2222-444i−4i00000022-2-22i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ6344-4-4-444-44004i−4i4i−4i004-4-4-444-40000000000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ6444-4-4-444-4400−4i4i−4i4i004-4-4-444-4000000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ6544-4-4-444-4-2004i−4i4i−4i00-2222-2-22000000000000000000−2i2i−2i2i−2i32i32i3−2i3000000002323−23−230000000000000000000000000000
χ6644-4-4-444-4-2004i−4i4i−4i00-2222-2-22000000000000000000−2i2i−2i2i2i3−2i3−2i32i300000000−23−2323230000000000000000000000000000
χ6744-4-4-444-4-200−4i4i−4i4i00-2222-2-220000000000000000002i−2i2i−2i−2i32i32i3−2i300000000−23−2323230000000000000000000000000000
χ6844-4-4-444-4-200−4i4i−4i4i00-2222-2-220000000000000000002i−2i2i−2i2i3−2i3−2i32i3000000002323−23−230000000000000000000000000000
χ694-444-4-44-444i−4i0000−4i4i-444-4-44-4000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ704-444-4-44-44−4i4i00004i−4i-444-4-44-400000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ714-444-4-44-4-24i−4i0000−4i4i2-2-222-2200000000000000−2i2i2i−2i00000000−2i32i3−2i32i3000023−2323−230000000000000000000000000000
χ724-444-4-44-4-24i−4i0000−4i4i2-2-222-2200000000000000−2i2i2i−2i000000002i3−2i32i3−2i30000−2323−23230000000000000000000000000000
χ734-444-4-44-4-2−4i4i00004i−4i2-2-222-22000000000000002i−2i−2i2i00000000−2i32i3−2i32i30000−2323−23230000000000000000000000000000
χ744-444-4-44-4-2−4i4i00004i−4i2-2-222-22000000000000002i−2i−2i2i000000002i3−2i32i3−2i3000023−2323−230000000000000000000000000000
χ754-44-444-4-44004i−4i−4i4i00-44-444-4-40000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ764-44-444-4-4400−4i4i4i−4i00-44-444-4-4000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ774-44-444-4-4-2004i−4i−4i4i002-22-2-2220000000000−2i32i3−2i32i30000−2i2i2i−2i000023−23−2323000000000000000000000000000000000000
χ784-44-444-4-4-2004i−4i−4i4i002-22-2-22200000000002i3−2i32i3−2i30000−2i2i2i−2i0000−232323−23000000000000000000000000000000000000
χ794-44-444-4-4-200−4i4i4i−4i002-22-2-2220000000000−2i32i3−2i32i300002i−2i−2i2i0000−232323−23000000000000000000000000000000000000
χ804-44-444-4-4-200−4i4i4i−4i002-22-2-22200000000002i3−2i32i3−2i300002i−2i−2i2i000023−23−2323000000000000000000000000000000000000
χ814-4-44-44-44-24444-4-4-4-422-22-22-20000004-4000000-22-22-2-22200000000-2-22200000000000000000000000000000000
χ824-4-44-44-44-244-4-444-4-422-22-22-2000000-44000000-22-2222-2-20000000022-2-200000000000000000000000000000000
χ834-4-44-44-44-2-4-444-4-44422-22-22-2000000-440000002-22-2-2-2220000000022-2-200000000000000000000000000000000
χ844-4-44-44-44-2-4-4-4-4444422-22-22-20000004-40000002-22-222-2-200000000-2-22200000000000000000000000000000000
χ854-4-4-44-444400000000-4-4-44-444000000004-40000000000000000000000004-4-440000000000000000000000000000
χ864-4-4-44-444400000000-4-4-44-44400000000-44000000000000000000000000-444-40000000000000000000000000000
χ874-4-4-44-444-200000000222-22-2-2000000004-4−2i32i32i3−2i300000000000000002i3−2i3−2i32i3-222-20000000000000000000000000000
χ884-4-4-44-444-200000000222-22-2-2000000004-42i3−2i3−2i32i30000000000000000−2i32i32i3−2i3-222-20000000000000000000000000000
χ894-4-4-44-444-200000000222-22-2-200000000-44−2i32i32i3−2i30000000000000000−2i32i32i3−2i32-2-220000000000000000000000000000
χ904-4-4-44-444-200000000222-22-2-200000000-442i3−2i3−2i32i300000000000000002i3−2i3−2i32i32-2-220000000000000000000000000000

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