Finite Group Databasebeta

← Group #10858104

Character table — Group #10858104

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121244444466121212121212121212121212121212124444441212121222444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
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
χ911111111111111111111-1-1-1-111-1-11111-1-1-1-11-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-111-1-111-1-1-1-111-1-111
χ1011111111111111111111-1-1-1-111-1-11111-1-1-1-11-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-11111-1-111-1-1
χ1111111111111111111111-1-1-1-111-1-11111-1-1-1-11-1-1-111-1-11111-1-11111-1-1-1-1-1-111111-111-1-1-1-111-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-111-1-11111-1-1-1-11-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111111111111-111-1-111-1-1-1-11111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1-1-11111-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-1-1-1-1-111111111-1-1-1-11111-11-1-11111-1-1-1-1-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-2-2-2-2-2-2-2000022-2-222220000-2-20000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22200002222-2-2-2-20000220000000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-22222-220000-2-2-2-222-2-20000220000000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-222-2-2-2-222222-20000-2-222-2-2220000-2-20000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-11111-1-111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-1111111-1-1-1-111-1-1-1-10000-2-2111100000000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-111112-222-2-211-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-111112-2-2-22211-1-1-1-111-1-1-1-111111100002-2-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-11111-2222-2-2111111-1-11111-1-1-1-1-1-100002-2-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-11111-22-2-222111111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2222211111111-2-20000-1-111-1-1-1-1−i3−i3i3i311−i3−i3i3i3000000−i3i3−i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2222211111111-2-20000-1-111-1-1-1-1i3i3−i3−i311i3i3−i3−i3000000i3−i3i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-211111111220000-1-1-1-11111−i3−i3i3i3-1-1−i3−i3i3i3000000i3−i3i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-211111111220000-1-1-1-11111i3i3−i3−i3-1-1i3i3−i3−i3000000−i3i3−i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-2200001111-1-111−i3−i3i3i3-1-1i3i3−i3−i3000000−i3i3i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-2200001111-1-111i3i3−i3−i3-1-1−i3−i3i3i3000000i3−i3−i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-12-2000011-1-111-1-1−i3−i3i3i311i3i3−i3−i3000000i3−i3−i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-12-2000011-1-111-1-1i3i3−i3−i311−i3−i3i3i3000000−i3i3i3−i300000000000000
χ3722-22-2-22-2222-2-222-22-2-2-22-22-2000022-2-222-2-20000002-2000000000000000000000000002-22-20000000000
χ3822-22-2-22-2222-2-222-22-2-2-22-22-2000022-2-222-2-20000002-200000000000000000000000000-22-220000000000
χ3922-22-2-22-2222-2-222-22-2-2-2-22-22000022-2-2-2-222000000-22000000000000000000000000002-2-220000000000
χ4022-22-2-22-2222-2-222-22-2-2-2-22-22000022-2-2-2-222000000-2200000000000000000000000000-222-20000000000
χ4122-22-2-22-22-2-22222-22-2-2-22-2-220000-2-222-2-2220000002-200000000000000002i2i−2i−2i00000000002i−2i00000000
χ4222-22-2-22-22-2-22222-22-2-2-22-2-220000-2-222-2-2220000002-20000000000000000−2i−2i2i2i0000000000−2i2i00000000
χ4322-22-2-22-22-2-22222-22-2-2-2-222-20000-2-22222-2-2000000-2200000000000000002i2i−2i−2i0000000000−2i2i00000000
χ4422-22-2-22-22-2-22222-22-2-2-2-222-20000-2-22222-2-2000000-220000000000000000−2i−2i2i2i00000000002i−2i00000000
χ452-2222-2-2-222-2-22-2-2222-2-2000000002-22-20000002i−2i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000002-20000
χ462-2222-2-2-222-2-22-2-2222-2-2000000002-22-20000002i−2i00000000000000002i−2i2i−2i−2i2i−2i2i00000000000000-220000
χ472-2222-2-2-222-2-22-2-2222-2-2000000002-22-2000000−2i2i0000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000-220000
χ482-2222-2-2-222-2-22-2-2222-2-2000000002-22-2000000−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000002-20000
χ492-2-22-22-222-22-22-2-2-22-22200000000-222-2000000002-2000000002-22-20000002-2-2200000000000000002-200
χ502-2-22-22-222-22-22-2-2-22-22200000000-222-2000000002-2000000002-22-2000000-222-20000000000000000-2200
χ512-2-22-22-222-22-22-2-2-22-22200000000-222-200000000-2200000000-22-220000002-2-220000000000000000-2200
χ522-2-22-22-222-22-22-2-2-22-22200000000-222-200000000-2200000000-22-22000000-222-200000000000000002-200
χ53444-4-4-4-44400004-44-4-44-400000000000000000000000000000000000000000000000000000000−2i22i2000000
χ54444-4-4-4-44400004-44-4-44-4000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ5544-44-4-44-4-244-4-4-2-22-22224-44-40000-2-222-2-222000000-220000000000000000000000000000000000000000
χ5644-44-4-44-4-244-4-4-2-22-2222-44-440000-2-22222-2-20000002-20000000000000000000000000000000000000000
χ5744-44-4-44-4-2-4-444-2-22-22224-4-44000022-2-222-2-2000000-220000000000000000000000000000000000000000
χ5844-44-4-44-4-2-4-444-2-22-2222-444-4000022-2-2-2-2220000002-20000000000000000000000000000000000000000
χ5944-4-444-4-4400004-4-4-44-4400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ6044-4-444-4-4400004-4-4-44-44000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ614-4444-4-4-44-444-4-4-4444-4-400000000-44-440000000000000000000000000000000000000000000000000000
χ624-4444-4-4-4-24-4-4422-2-2-22200000000-22-220000004i−4i0000000000000000−2i2i−2i2i000000000000000000000000
χ634-4444-4-4-4-24-4-4422-2-2-22200000000-22-22000000−4i4i00000000000000002i−2i2i−2i000000000000000000000000
χ644-4444-4-4-4-2-444-422-2-2-222000000002-22-200000000000000000000000023−23−2323000000000000000000000000
χ654-4444-4-4-4-2-444-422-2-2-222000000002-22-2000000000000000000000000−232323−23000000000000000000000000
χ664-44-4-444-440000-444-4-4-440000004i−4i000000000000000000004i−4i0000000000000000000000000000000000
χ674-44-4-444-440000-444-4-4-44000000−4i4i00000000000000000000−4i4i0000000000000000000000000000000000
χ684-44-4-444-4-200002-2-2222-20000004i−4i000023−2323−2300000000−2i32i300−2i2i0000000000000000000000000000000000
χ694-44-4-444-4-200002-2-2222-20000004i−4i0000−2323−2323000000002i3−2i300−2i2i0000000000000000000000000000000000
χ704-44-4-444-4-200002-2-2222-2000000−4i4i000023−2323−23000000002i3−2i3002i−2i0000000000000000000000000000000000
χ714-44-4-444-4-200002-2-2222-2000000−4i4i0000−2323−232300000000−2i32i3002i−2i0000000000000000000000000000000000
χ724-4-44-44-4444-44-4-4-4-44-444000000004-4-440000000000000000000000000000000000000000000000000000
χ734-4-44-44-44-24-44-4222-22-2-200000000-222-2000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ744-4-44-44-44-24-44-4222-22-2-200000000-222-20000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ754-4-44-44-44-2-44-44222-22-2-2000000002-2-22000000004-400000000-22-22000000000000000000000000000000
χ764-4-44-44-44-2-44-44222-22-2-2000000002-2-2200000000-44000000002-22-2000000000000000000000000000000
χ774-4-4-44-44440000-44-4-444-400004-4000000000000000000004-4000000000000000000000000000000000000
χ784-4-4-44-44440000-44-4-444-40000-4400000000000000000000-44000000000000000000000000000000000000
χ794-4-4-44-444-200002-222-2-2200004-400000023−23−23230000000000-2200000023−230000000000000000000000000000
χ804-4-4-44-444-200002-222-2-2200004-4000000−232323−230000000000-22000000−23230000000000000000000000000000
χ814-4-4-44-444-200002-222-2-220000-4400000023−23−232300000000002-2000000−23230000000000000000000000000000
χ824-4-4-44-444-200002-222-2-220000-44000000−232323−2300000000002-200000023−230000000000000000000000000000
χ83888-8-8-8-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-888-8-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000

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