Finite Group Databasebeta

← Group #10690768

Character table — Group #10690768

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222222222234444666666644444444446666121212121212121212121212121212121212121212121212444412121212121212124444444488888888
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
χ5111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-222222222222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2722222222-2-2-2-222222222222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-2-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-2-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ3722-22-2-22-2000022i−2i2i−2i2-22-2-22-2002i−2i002-200000000002i2i−2i−2i00002i2i−2i−2i22-2-200000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ3822-22-2-22-2000022i−2i2i−2i2-22-2-22-2002i−2i002-200000000002i2i−2i−2i00002i2i−2i−2i22-2-20000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ3922-22-2-22-2000022i−2i2i−2i2-22-2-22-200−2i2i00-220000000000−2i−2i2i2i00002i2i−2i−2i-2-22200000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ4022-22-2-22-2000022i−2i2i−2i2-22-2-22-200−2i2i00-220000000000−2i−2i2i2i00002i2i−2i−2i-2-2220000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ4122-22-2-22-200002−2i2i−2i2i2-22-2-22-2002i−2i00-2200000000002i2i−2i−2i0000−2i−2i2i2i-2-22200000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ4222-22-2-22-200002−2i2i−2i2i2-22-2-22-2002i−2i00-2200000000002i2i−2i−2i0000−2i−2i2i2i-2-2220000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ4322-22-2-22-200002−2i2i−2i2i2-22-2-22-200−2i2i002-20000000000−2i−2i2i2i0000−2i−2i2i2i22-2-200000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ4422-22-2-22-200002−2i2i−2i2i2-22-2-22-200−2i2i002-20000000000−2i−2i2i2i0000−2i−2i2i2i22-2-20000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ452-2-2-22-2222-22-2222-2-2-2-2-22-22200002-2000022-2-20000000022-2-22-22-200000000000000000000000000002i−2i2i−2i0000
χ462-2-2-22-2222-22-2222-2-2-2-2-22-22200002-2000022-2-20000000022-2-22-22-20000000000000000000000000000−2i2i−2i2i0000
χ472-2-2-22-2222-22-22-2-222-2-2-22-2220000-22000022-2-200000000-2-222-22-22000000000000000000000000000000002-22-2
χ482-2-2-22-2222-22-22-2-222-2-2-22-2220000-22000022-2-200000000-2-222-22-2200000000000000000000000000000000-22-22
χ492-2-2-22-222-22-22222-2-2-2-2-22-2220000-220000-2-22200000000-2-2222-22-2000000000000000000000000000000002i−2i−2i2i
χ502-2-2-22-222-22-22222-2-2-2-2-22-2220000-220000-2-22200000000-2-2222-22-200000000000000000000000000000000−2i2i2i−2i
χ512-2-2-22-222-22-222-2-222-2-2-22-22200002-20000-2-2220000000022-2-2-22-2200000000000000000000000000002-2-220000
χ522-2-2-22-222-22-222-2-222-2-2-22-22200002-20000-2-2220000000022-2-2-22-220000000000000000000000000000-222-20000
χ53444-44-4-4-44-4-444000044-44-4-4-400000000004-44-40000000000000000000000000000000000000000000000000000
χ54444-44-4-4-44-4-44-20000-2-22-22220000000000-22-22−2i3−2i32i32i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ55444-44-4-4-44-4-44-20000-2-22-22220000000000-22-222i32i3−2i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ56444-44-4-4-4-444-44000044-44-4-4-40000000000-44-440000000000000000000000000000000000000000000000000000
χ57444-44-4-4-4-444-4-20000-2-22-222200000000002-22-2−2i3−2i32i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ58444-44-4-4-4-444-4-20000-2-22-222200000000002-22-22i32i3−2i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ5944-44-4-44-40000-24i−4i4i−4i-22-222-22004i−4i004-40000000000−2i−2i2i2i0000−2i−2i2i2i-2-22200000000000000000000000000000000
χ6044-44-4-44-40000-24i−4i4i−4i-22-222-2200−4i4i00-4400000000002i2i−2i−2i0000−2i−2i2i2i22-2-200000000000000000000000000000000
χ6144-44-4-44-40000-2−4i4i−4i4i-22-222-22004i−4i00-440000000000−2i−2i2i2i00002i2i−2i−2i22-2-200000000000000000000000000000000
χ6244-44-4-44-40000-2−4i4i−4i4i-22-222-2200−4i4i004-400000000002i2i−2i−2i00002i2i−2i−2i-2-22200000000000000000000000000000000
χ6344-4-4-44-440000400004-4-4-44-44000000004i−4i0000000000000000000000004i4i−4i−4i0000000000000000000000000000
χ6444-4-4-44-440000400004-4-4-44-4400000000−4i4i000000000000000000000000−4i−4i4i4i0000000000000000000000000000
χ6544-4-4-44-440000-20000-2222-22-2000000004i−4i0000000023−23−2323−2i32i3−2i32i300000000−2i−2i2i2i0000000000000000000000000000
χ6644-4-4-44-440000-20000-2222-22-2000000004i−4i00000000−232323−232i3−2i32i3−2i300000000−2i−2i2i2i0000000000000000000000000000
χ6744-4-4-44-440000-20000-2222-22-200000000−4i4i0000000023−23−23232i3−2i32i3−2i3000000002i2i−2i−2i0000000000000000000000000000
χ6844-4-4-44-440000-20000-2222-22-200000000−4i4i00000000−232323−23−2i32i3−2i32i3000000002i2i−2i−2i0000000000000000000000000000
χ694-444-4-4-44000040000-444-4-4-444i−4i0000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ704-444-4-4-44000040000-444-4-4-44−4i4i000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ714-444-4-4-440000-200002-2-2222-24i−4i000000000000−2i2i−2i2i0000−2i32i32i3−2i3000023−2323−2300000000000000000000000000000000
χ724-444-4-4-440000-200002-2-2222-24i−4i000000000000−2i2i−2i2i00002i3−2i3−2i32i30000−2323−232300000000000000000000000000000000
χ734-444-4-4-440000-200002-2-2222-2−4i4i0000000000002i−2i2i−2i0000−2i32i32i3−2i30000−2323−232300000000000000000000000000000000
χ744-444-4-4-440000-200002-2-2222-2−4i4i0000000000002i−2i2i−2i00002i3−2i3−2i32i3000023−2323−2300000000000000000000000000000000
χ754-44-4-444-4000044i−4i−4i4i-44-4-444-4000000000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ764-44-4-444-400004−4i4i4i−4i-44-4-444-400000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ774-44-4-444-40000-24i−4i−4i4i2-222-2-220000000000000023−23−232300000000−2i2i2i−2i0000−2i32i3−2i32i30000000000000000000000000000
χ784-44-4-444-40000-24i−4i−4i4i2-222-2-2200000000000000−232323−2300000000−2i2i2i−2i00002i3−2i32i3−2i30000000000000000000000000000
χ794-44-4-444-40000-2−4i4i4i−4i2-222-2-220000000000000023−23−2323000000002i−2i−2i2i00002i3−2i32i3−2i30000000000000000000000000000
χ804-44-4-444-40000-2−4i4i4i−4i2-222-2-2200000000000000−232323−23000000002i−2i−2i2i0000−2i32i3−2i32i30000000000000000000000000000
χ814-4-4444-4-444-4-440000-4-4444-4-400000000004-4-440000000000000000000000000000000000000000000000000000
χ824-4-4444-4-444-4-4-2000022-2-2-2220000000000-222-2000000000000000023−23−232323−23−23230000000000000000000000000000
χ834-4-4444-4-444-4-4-2000022-2-2-2220000000000-222-20000000000000000−232323−23−232323−230000000000000000000000000000
χ844-4-4444-4-4-4-44440000-4-4444-4-40000000000-444-40000000000000000000000000000000000000000000000000000
χ854-4-4444-4-4-4-444-2000022-2-2-22200000000002-2-22000000000000000023−23−2323−232323−230000000000000000000000000000
χ864-4-4444-4-4-4-444-2000022-2-2-22200000000002-2-220000000000000000−232323−2323−23−23230000000000000000000000000000
χ874-4-4-44-4444-44-4-244-4-4222-22-2-200004-40000-2-22200000000-2-222-22-22000000000000000000000000000000000000
χ884-4-4-44-4444-44-4-2-4-444222-22-2-20000-440000-2-2220000000022-2-22-22-2000000000000000000000000000000000000
χ894-4-4-44-444-44-44-244-4-4222-22-2-20000-44000022-2-20000000022-2-2-22-22000000000000000000000000000000000000
χ904-4-4-44-444-44-44-2-4-444222-22-2-200004-4000022-2-200000000-2-2222-22-2000000000000000000000000000000000000

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