Finite Group Databasebeta

← Group #10690778

Character table — Group #10690778

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222222222344446666666444444444466661212121212121212121212121212121212121212121212122444661212121212124444444488888888
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
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
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
χ21222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111112-2-22-1-11111-1-10000000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-222-211-1-1-1-1110000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000i3−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−i3i3i3−i3i3−i3−i3i30000000000000000
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−i3−i3i3−i3i3i3−i30000000000000000
χ2722222222-2-2-2-2222222222222-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-22222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-22222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-1111122-2-2-1-1-1-111110000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-11111-2-2221111-1-1-1-10000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-12-22-2-1-111-1-1110000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-1-22-2211-1-111-1-10000000000000000
χ3722-222-2-2-2000022i−2i2i−2i2-222-2-2-200002-22i−2i00000000002i2i−2i−2i000022-2-22i2i−2i−2i00000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ3822-222-2-2-2000022i−2i2i−2i2-222-2-2-200002-22i−2i00000000002i2i−2i−2i000022-2-22i2i−2i−2i0000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ3922-222-2-2-2000022i−2i2i−2i2-222-2-2-20000-22−2i2i00000000002i2i−2i−2i0000-2-222−2i−2i2i2i00000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ4022-222-2-2-2000022i−2i2i−2i2-222-2-2-20000-22−2i2i00000000002i2i−2i−2i0000-2-222−2i−2i2i2i0000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ4122-222-2-2-200002−2i2i−2i2i2-222-2-2-200002-2−2i2i0000000000−2i−2i2i2i000022-2-2−2i−2i2i2i00000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ4222-222-2-2-200002−2i2i−2i2i2-222-2-2-200002-2−2i2i0000000000−2i−2i2i2i000022-2-2−2i−2i2i2i0000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ4322-222-2-2-200002−2i2i−2i2i2-222-2-2-20000-222i−2i0000000000−2i−2i2i2i0000-2-2222i2i−2i−2i00000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ4422-222-2-2-200002−2i2i−2i2i2-222-2-2-20000-222i−2i0000000000−2i−2i2i2i0000-2-2222i2i−2i−2i0000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ452-2-22-22-222-22-2222-2-2-2-22-22-222-20000000022-2-222-2-22-22-200000000000000000000000000000000000000002i−2i2i−2i
χ462-2-22-22-222-22-2222-2-2-2-22-22-222-20000000022-2-222-2-22-22-20000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-22-22-222-22-22-2-222-2-22-22-22-220000000022-2-2-2-222-22-220000000000000000000000000000000000002-22-20000
χ482-2-22-22-222-22-22-2-222-2-22-22-22-220000000022-2-2-2-222-22-22000000000000000000000000000000000000-22-220000
χ492-2-22-22-22-22-22222-2-2-2-22-22-22-2200000000-2-222-2-2222-22-20000000000000000000000000000000000002i−2i−2i2i0000
χ502-2-22-22-22-22-22222-2-2-2-22-22-22-2200000000-2-222-2-2222-22-2000000000000000000000000000000000000−2i2i2i−2i0000
χ512-2-22-22-22-22-222-2-222-2-22-22-222-200000000-2-22222-2-2-22-2200000000000000000000000000000000000000002-2-22
χ522-2-22-22-22-22-222-2-222-2-22-22-222-200000000-2-22222-2-2-22-220000000000000000000000000000000000000000-222-2
χ53444-4-4-4-4444-4-44000044-4-4-4-4400000000004-44-40000000000000000000000000000000000000000000000000000
χ54444-4-4-4-4444-4-4-20000-2-22222-20000000000-22-22000000002323−23−2323−2323−23000000000000000000000000000000000000
χ55444-4-4-4-4444-4-4-20000-2-22222-20000000000-22-2200000000−23−232323−2323−2323000000000000000000000000000000000000
χ56444-4-4-4-44-4-4444000044-4-4-4-440000000000-44-440000000000000000000000000000000000000000000000000000
χ57444-4-4-4-44-4-444-20000-2-22222-200000000002-22-2000000002323−23−23−2323−2323000000000000000000000000000000000000
χ58444-4-4-4-44-4-444-20000-2-22222-200000000002-22-200000000−23−23232323−2323−23000000000000000000000000000000000000
χ5944-444-4-4-40000-24i−4i4i−4i-22-2-222200004-44i−4i0000000000−2i−2i2i2i0000-2-222−2i−2i2i2i00000000000000000000000000000000
χ6044-444-4-4-40000-24i−4i4i−4i-22-2-22220000-44−4i4i0000000000−2i−2i2i2i000022-2-22i2i−2i−2i00000000000000000000000000000000
χ6144-444-4-4-40000-2−4i4i−4i4i-22-2-222200004-4−4i4i00000000002i2i−2i−2i0000-2-2222i2i−2i−2i00000000000000000000000000000000
χ6244-444-4-4-40000-2−4i4i−4i4i-22-2-22220000-444i−4i00000000002i2i−2i−2i000022-2-2−2i−2i2i2i00000000000000000000000000000000
χ6344-4-4-444-40000400004-4-4-444-4000000004i−4i0000000000000000000000004i4i−4i−4i0000000000000000000000000000
χ6444-4-4-444-40000400004-4-4-444-400000000−4i4i000000000000000000000000−4i−4i4i4i0000000000000000000000000000
χ6544-4-4-444-40000-20000-2222-2-22000000004i−4i0000−2i32i3−2i32i30000000023−23−23230000−2i−2i2i2i0000000000000000000000000000
χ6644-4-4-444-40000-20000-2222-2-22000000004i−4i00002i3−2i32i3−2i300000000−232323−230000−2i−2i2i2i0000000000000000000000000000
χ6744-4-4-444-40000-20000-2222-2-2200000000−4i4i0000−2i32i3−2i32i300000000−232323−2300002i2i−2i−2i0000000000000000000000000000
χ6844-4-4-444-40000-20000-2222-2-2200000000−4i4i00002i3−2i32i3−2i30000000023−23−232300002i2i−2i−2i0000000000000000000000000000
χ694-444-4-44-4000044i−4i−4i4i-444-4-44-40000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ704-444-4-44-400004−4i4i4i−4i-444-4-44-4000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ714-444-4-44-40000-24i−4i−4i4i2-2-222-22000000000000000000−2i2i2i−2i−2i32i3−2i32i30000000023−2323−230000000000000000000000000000
χ724-444-4-44-40000-24i−4i−4i4i2-2-222-22000000000000000000−2i2i2i−2i2i3−2i32i3−2i300000000−2323−23230000000000000000000000000000
χ734-444-4-44-40000-2−4i4i4i−4i2-2-222-220000000000000000002i−2i−2i2i−2i32i3−2i32i300000000−2323−23230000000000000000000000000000
χ744-444-4-44-40000-2−4i4i4i−4i2-2-222-220000000000000000002i−2i−2i2i2i3−2i32i3−2i30000000023−2323−230000000000000000000000000000
χ754-44-444-4-4000040000-44-444-4-4004i−4i0000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ764-44-444-4-4000040000-44-444-4-400−4i4i000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ774-44-444-4-40000-200002-22-2-222004i−4i0000000000−2i32i32i3−2i30000−2i2i2i−2i000023−2323−2300000000000000000000000000000000
χ784-44-444-4-40000-200002-22-2-222004i−4i00000000002i3−2i3−2i32i30000−2i2i2i−2i0000−2323−232300000000000000000000000000000000
χ794-44-444-4-40000-200002-22-2-22200−4i4i0000000000−2i32i32i3−2i300002i−2i−2i2i0000−2323−232300000000000000000000000000000000
χ804-44-444-4-40000-200002-22-2-22200−4i4i00000000002i3−2i3−2i32i300002i−2i−2i2i000023−2323−2300000000000000000000000000000000
χ814-4-44-44-444-44-4-244-4-422-22-22-24-400000000-2-222-2-222-22-2200000000000000000000000000000000000000000000
χ824-4-44-44-444-44-4-2-4-44422-22-22-2-4400000000-2-22222-2-22-22-200000000000000000000000000000000000000000000
χ834-4-44-44-44-44-44-244-4-422-22-22-2-440000000022-2-222-2-2-22-2200000000000000000000000000000000000000000000
χ844-4-44-44-44-44-44-2-4-44422-22-22-24-40000000022-2-2-2-2222-22-200000000000000000000000000000000000000000000
χ854-4-4-44-4444-4-4440000-4-4-44-44400000000004-4-440000000000000000000000000000000000000000000000000000
χ864-4-4-44-4444-4-44-20000222-22-2-20000000000-222-20000000000000000−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000
χ874-4-4-44-4444-4-44-20000222-22-2-20000000000-222-200000000000000002i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000
χ884-4-4-44-444-444-440000-4-4-44-4440000000000-444-40000000000000000000000000000000000000000000000000000
χ894-4-4-44-444-444-4-20000222-22-2-200000000002-2-220000000000000000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000
χ904-4-4-44-444-444-4-20000222-22-2-200000000002-2-2200000000000000002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000

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