Finite Group Databasebeta

← Group #10853236

Character table — Group #10853236

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121244444466121212121212121212121212121212124444441212121244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-111-1-11111-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-111-1-1-1-111-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-111-1-11111-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-1-1-11111
χ1111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-111111111-11-1-111-1-111-1-1-1-1-1-11111
χ1211111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-1111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-11111-1-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111111111111-111-1-111-1-1-1-111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1-1-11111-1-111-1-111
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-2-2-2-2-200-2-20022-2-222220000-2-20000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20022002222-2-2-2-20000220000000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2222200-2200-2-2-2-222-2-20000220000000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-222-2-2-2-22222002-200-2-222-2-2220000-2-20000000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-11111-1-111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-122-2-222-1-1111111-1-1-1-111-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-11111222-2-2-211-1-1-1-111-1-1-1-111111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-11111-2-22-22211-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-1111122-22-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-11111-2-2-2222111111-1-11111-1-1-1-1-1-100002-2-1-11100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222221111111100-2-200-1-111-1-1-1-1−i3−i3i3i311−i3−i3i3i3000000−i3i3−i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222221111111100-2-200-1-111-1-1-1-1i3i3−i3−i311i3i3−i3−i3000000i3−i3i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-211111111002200-1-1-1-11111−i3−i3i3i3-1-1−i3−i3i3i3000000i3−i3i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-211111111002200-1-1-1-11111i3i3−i3−i3-1-1i3i3−i3−i3000000−i3i3−i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-100-22001111-1-111−i3−i3i3i3-1-1i3i3−i3−i3000000−i3i3i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-100-22001111-1-111i3i3−i3−i3-1-1−i3−i3i3i3000000i3−i3−i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1002-20011-1-111-1-1−i3−i3i3i311i3i3−i3−i3000000i3−i3−i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1002-20011-1-111-1-1i3i3−i3−i311−i3−i3i3i3000000−i3i3i3−i300000000000000
χ37222-2-2-2-22222-2-222-22-2-2-22-22-2000022-2-222-2-20000002-2000000000000000022-2-200000000002-200000000
χ38222-2-2-2-22222-2-222-22-2-2-22-22-2000022-2-222-2-20000002-20000000000000000-2-2220000000000-2200000000
χ39222-2-2-2-22222-2-222-22-2-2-2-22-22000022-2-2-2-222000000-22000000000000000022-2-20000000000-2200000000
χ40222-2-2-2-22222-2-222-22-2-2-2-22-22000022-2-2-2-222000000-220000000000000000-2-22200000000002-200000000
χ41222-2-2-2-222-2-22222-22-2-2-22-2-220000-2-222-2-2220000002-2000000000000000000000000002i−2i2i−2i0000000000
χ42222-2-2-2-222-2-22222-22-2-2-22-2-220000-2-222-2-2220000002-200000000000000000000000000−2i2i−2i2i0000000000
χ43222-2-2-2-222-2-22222-22-2-2-2-222-20000-2-22222-2-2000000-22000000000000000000000000002i−2i−2i2i0000000000
χ44222-2-2-2-222-2-22222-22-2-2-2-222-20000-2-22222-2-2000000-2200000000000000000000000000−2i2i2i−2i0000000000
χ452-222-22-2-222-2-22-2-2222-2-2000000002-22-2000000002i−2i000000000000002i−2i2i−2i2i−2i2i−2i00000000000000002-200
χ462-222-22-2-222-2-22-2-2222-2-2000000002-22-2000000002i−2i000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000-2200
χ472-222-22-2-222-2-22-2-2222-2-2000000002-22-200000000−2i2i00000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000-2200
χ482-222-22-2-222-2-22-2-2222-2-2000000002-22-200000000−2i2i00000000000000−2i2i−2i2i−2i2i−2i2i00000000000000002-200
χ492-22-22-22-222-22-2-2-2-22-222000000002-2-2200002-20000000000002-22-20000002i−2i−2i2i000000000000002i−2i0000
χ502-22-22-22-222-22-2-2-2-22-222000000002-2-2200002-20000000000002-22-2000000−2i2i2i−2i00000000000000−2i2i0000
χ512-22-22-22-222-22-2-2-2-22-222000000002-2-220000-22000000000000-22-220000002i−2i−2i2i00000000000000−2i2i0000
χ522-22-22-22-222-22-2-2-2-22-222000000002-2-220000-22000000000000-22-22000000−2i2i2i−2i000000000000002i−2i0000
χ53444-4-4-4-44-244-4-4-2-22-22224-44-40000-2-222-2-222000000-220000000000000000000000000000000000000000
χ54444-4-4-4-44-244-4-4-2-22-2222-44-440000-2-22222-2-20000002-20000000000000000000000000000000000000000
χ55444-4-4-4-44-2-4-444-2-22-22224-4-44000022-2-222-2-2000000-220000000000000000000000000000000000000000
χ56444-4-4-4-44-2-4-444-2-22-2222-444-4000022-2-2-2-2220000002-20000000000000000000000000000000000000000
χ5744-444-4-4-4400004-4-4-444-400004-4000000000000000000004-4000000000000000000000000000000000000
χ5844-444-4-4-4400004-4-4-444-40000-4400000000000000000000-44000000000000000000000000000000000000
χ5944-444-4-4-4-20000-2222-2-2200004-400000023−2323−230000000000-2200000023−230000000000000000000000000000
χ6044-444-4-4-4-20000-2222-2-2200004-4000000−2323−23230000000000-22000000−23230000000000000000000000000000
χ6144-444-4-4-4-20000-2222-2-220000-4400000023−2323−2300000000002-2000000−23230000000000000000000000000000
χ6244-444-4-4-4-20000-2222-2-220000-44000000−2323−232300000000002-200000023−230000000000000000000000000000
χ6344-4-4-444-4400004-44-4-4-440000004i−4i000000000000000000004i−4i0000000000000000000000000000000000
χ6444-4-4-444-4400004-44-4-4-44000000−4i4i00000000000000000000−4i4i0000000000000000000000000000000000
χ6544-4-4-444-4-20000-22-2222-20000004i−4i000023−23−232300000000−2i32i300−2i2i0000000000000000000000000000000000
χ6644-4-4-444-4-20000-22-2222-20000004i−4i0000−232323−23000000002i3−2i300−2i2i0000000000000000000000000000000000
χ6744-4-4-444-4-20000-22-2222-2000000−4i4i000023−23−2323000000002i3−2i3002i−2i0000000000000000000000000000000000
χ6844-4-4-444-4-20000-22-2222-2000000−4i4i0000−232323−2300000000−2i32i3002i−2i0000000000000000000000000000000000
χ694-444-44-4-44-444-4-4-4444-4-400000000-44-440000000000000000000000000000000000000000000000000000
χ704-444-44-4-4-24-4-4422-2-2-22200000000-22-22000000004i−4i00000000000000−2i2i−2i2i000000000000000000000000
χ714-444-44-4-4-24-4-4422-2-2-22200000000-22-2200000000−4i4i000000000000002i−2i2i−2i000000000000000000000000
χ724-444-44-4-4-2-444-422-2-2-222000000002-22-200000000000000000000000023−23−2323000000000000000000000000
χ734-444-44-4-4-2-444-422-2-2-222000000002-22-2000000000000000000000000−232323−23000000000000000000000000
χ744-44-44-44-44-44-44-4-4-44-44400000000-444-40000000000000000000000000000000000000000000000000000
χ754-44-44-44-4-24-44-4222-22-2-200000000-222-200004-4000000000000-22-22000000000000000000000000000000
χ764-44-44-44-4-24-44-4222-22-2-200000000-222-20000-440000000000002-22-2000000000000000000000000000000
χ774-44-44-44-4-2-44-44222-22-2-2000000002-2-22000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ784-44-44-44-4-2-44-44222-22-2-2000000002-2-220000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ794-4-44-4-44440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000022−22
χ804-4-44-4-44440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000000−2222
χ814-4-4-444-4440000-444-4-44-400000000000000000000000000000000000000000000000000000000−2i22i2000000
χ824-4-4-444-4440000-444-4-44-4000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ838-8-88-8-888-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000

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