Finite Group Databasebeta

← Group #10840226

Character table — Group #10840226

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121222244466666666121212121212121212124444441212121244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-11111-1-111-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111111111-11-1-111-1-1-1-111-1-111-1-111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-1111111-1-111-1-111-1-1
χ911111111111111111111-1-11111-1-111111111-111-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-11111-1-111111111-111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1211111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-11-1-111-1-111-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-111-1-1-1-111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-111-1-111-1-11111-1-1-1-111
χ17222222222-2-2-2-222222222222-2-222-2-2-2-2-2-2-2-2-200-20022-2-2000022-2-2220000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-222-2-2-2-2-2-22222200-20022220000-2-2-2-2-2-20000000000000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2200200-2-22200002222-2-20000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-22222-200200-2-2-2-20000-2-222220000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-11111-1-1-1-1-1-111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-11111-2222-2-2-1-111-1-1-1-111-1-111111100002-2-1-11100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-11111-2-2-2222-1-111111111-1-111-1-1-1-10000-2211-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-222-2221111-1-1-1-1-1-11111-1-1-1-10000-2-2111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111-1-111111111000022-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-11111222-2-2-211-1-1-1-1-1-11111-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-111112-2-2-22211-1-111111111-1-1-1-1-1-100002-2-1-11100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-22211111111-200-200-1-111−i3−i3i3i3-1-111-1-1−i3−i3i3i3000000−i3i3−i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-22211111111-200-200-1-111i3i3−i3−i3-1-111-1-1i3i3−i3−i3000000i3−i3i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-1200-200-1-1-1-1−i3−i3i3i3111111i3i3−i3−i3000000−i3i3i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-1200-200-1-1-1-1i3i3−i3−i3111111−i3−i3i3i3000000i3−i3−i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-21111111120020011-1-1−i3−i3i3i3-1-1-1-111−i3−i3i3i3000000i3−i3i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-21111111120020011-1-1i3i3−i3−i3-1-1-1-111i3i3−i3−i3000000−i3i3−i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2002001111−i3−i3i3i311-1-1-1-1i3i3−i3−i3000000i3−i3−i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2002001111i3i3−i3−i311-1-1-1-1−i3−i3i3i3000000−i3i3i3−i300000000000000
χ372222-2-2-2-222-2-22-2-2-2222-2002-22-20022-2-222-2-2000000000000002-2000000002i2i−2i−2i0000002i−2i000000000000
χ382222-2-2-2-222-2-22-2-2-2222-2002-22-20022-2-222-2-2000000000000002-200000000−2i−2i2i2i000000−2i2i000000000000
χ392222-2-2-2-222-2-22-2-2-2222-200-22-220022-2-2-2-22200000000000000-22000000002i2i−2i−2i000000−2i2i000000000000
χ402222-2-2-2-222-2-22-2-2-2222-200-22-220022-2-2-2-22200000000000000-2200000000−2i−2i2i2i0000002i−2i000000000000
χ412222-2-2-2-22-222-2-2-2-2222-2002-2-2200-2-222-2-222000000000000002-2000000000000000000002i−2i2i−2i00000000
χ422222-2-2-2-22-222-2-2-2-2222-2002-2-2200-2-222-2-222000000000000002-200000000000000000000−2i2i−2i2i00000000
χ432222-2-2-2-22-222-2-2-2-2222-200-222-200-2-22222-2-200000000000000-22000000000000000000002i−2i−2i2i00000000
χ442222-2-2-2-22-222-2-2-2-2222-200-222-200-2-22222-2-200000000000000-2200000000000000000000−2i2i2i−2i00000000
χ452-22-222-2-2222-2-22-2-2-22-22000000002-22-2000002-200000002-22-200000000002i−2i2i−2i0000000000002i−2i000000
χ462-22-222-2-2222-2-22-2-2-22-22000000002-22-2000002-200000002-22-20000000000−2i2i−2i2i000000000000−2i2i000000
χ472-22-222-2-2222-2-22-2-2-22-22000000002-22-200000-220000000-22-2200000000002i−2i2i−2i000000000000−2i2i000000
χ482-22-222-2-2222-2-22-2-2-22-22000000002-22-200000-220000000-22-220000000000−2i2i−2i2i0000000000002i−2i000000
χ492-22-2-2-22222-22-2-222-22-2-2000000002-2-22000000002i−2i000000000000002i−2i2i−2i2-2-22000000000000002i−2i0000
χ502-22-2-2-22222-22-2-222-22-2-2000000002-2-22000000002i−2i000000000000002i−2i2i−2i-222-200000000000000−2i2i0000
χ512-22-2-2-22222-22-2-222-22-2-2000000002-2-2200000000−2i2i00000000000000−2i2i−2i2i2-2-2200000000000000−2i2i0000
χ522-22-2-2-22222-22-2-222-22-2-2000000002-2-2200000000−2i2i00000000000000−2i2i−2i2i-222-2000000000000002i−2i0000
χ534444-4-4-4-4-24-4-44222-2-2-22004-44-400-2-222-2-22200000000000000-2200000000000000000000000000000000
χ544444-4-4-4-4-24-4-44222-2-2-2200-44-4400-2-22222-2-2000000000000002-200000000000000000000000000000000
χ554444-4-4-4-4-2-444-4222-2-2-22004-4-440022-2-222-2-200000000000000-2200000000000000000000000000000000
χ564444-4-4-4-4-2-444-4222-2-2-2200-444-40022-2-2-2-222000000000000002-200000000000000000000000000000000
χ5744-4-44-44-440000-44-44-4-44000000000000000000000000000000000000000000000000000000000000−2i22i200
χ5844-4-44-44-440000-44-44-4-440000000000000000000000000000000000000000000000000000000000002i2−2i200
χ5944-4-4-44-44400004-444-4-4-400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ6044-4-4-44-44400004-444-4-4-4000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ614-44-444-4-44-4-4444-4-4-44-4400000000-44-440000000000000000000000000000000000000000000000000000
χ624-44-444-4-4-244-4-4-2222-22-200000000-22-22000004-40000000-22-220000000000000000000000000000000000
χ634-44-444-4-4-244-4-4-2222-22-200000000-22-2200000-4400000002-22-20000000000000000000000000000000000
χ644-44-444-4-4-2-4-444-2222-22-2000000002-22-200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ654-44-444-4-4-2-4-444-2222-22-2000000002-22-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ664-44-4-4-4444-44-44-444-44-4-400000000-444-40000000000000000000000000000000000000000000000000000
χ674-44-4-4-444-24-44-42-2-22-22200000000-222-2000000004i−4i00000000000000−2i2i−2i2i000000000000000000000000
χ684-44-4-4-444-24-44-42-2-22-22200000000-222-200000000−4i4i000000000000002i−2i2i−2i000000000000000000000000
χ694-44-4-4-444-2-44-442-2-22-222000000002-2-2200000000000000000000000023−23−2323000000000000000000000000
χ704-44-4-4-444-2-44-442-2-22-222000000002-2-22000000000000000000000000−232323−23000000000000000000000000
χ714-4-444-4-4440000-4-44-4-4444-4000000000000000000004-40000000000000000000000000000000000000000
χ724-4-444-4-4440000-4-44-4-444-4400000000000000000000-440000000000000000000000000000000000000000
χ734-4-444-4-44-2000022-222-2-24-40000000000−2i32i3−2i32i3000000-22−2i32i300000000000000000000000000000000000000
χ744-4-444-4-44-2000022-222-2-24-400000000002i3−2i32i3−2i3000000-222i3−2i300000000000000000000000000000000000000
χ754-4-444-4-44-2000022-222-2-2-440000000000−2i32i3−2i32i30000002-22i3−2i300000000000000000000000000000000000000
χ764-4-444-4-44-2000022-222-2-2-4400000000002i3−2i32i3−2i30000002-2−2i32i300000000000000000000000000000000000000
χ774-4-44-444-44000044-4-4-44-40000004i−4i000000000000000000000000004i−4i0000000000000000000000000000
χ784-4-44-444-44000044-4-4-44-4000000−4i4i00000000000000000000000000−4i4i0000000000000000000000000000
χ794-4-44-444-4-20000-2-2222-220000004i−4i0000−2i32i32i3−2i3000000000000000023−23−2i2i0000000000000000000000000000
χ804-4-44-444-4-20000-2-2222-220000004i−4i00002i3−2i3−2i32i30000000000000000−2323−2i2i0000000000000000000000000000
χ814-4-44-444-4-20000-2-2222-22000000−4i4i0000−2i32i32i3−2i30000000000000000−23232i−2i0000000000000000000000000000
χ824-4-44-444-4-20000-2-2222-22000000−4i4i00002i3−2i3−2i32i3000000000000000023−232i−2i0000000000000000000000000000
χ8388-8-88-88-8-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000

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