Finite Group Databasebeta

← Group #10845512

Character table — Group #10845512

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344446666666224444441212121212121212244444666612121212121212121212121212128888888844121212122244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-111-1-1111111111-111-1-111-1-1-1-1-1-1-11
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111111-1
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111111-11-1-111-1-111-1-1-1-11-1
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-11
χ911111111111111111111-1-1-1-1111111111111-111-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ1011111111111111111111-1-1-1-1111111111111-111-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-111-1-11111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-11-111-1-1-1-111-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-111-1-1-1-1-1-11111-1-111-1-1-1-111111-111-1-111-1-111-1-11-1
χ17222222222-2-2-2-2222222222-2-222-2-2-2-2-2-22222200-2002222-2-200000000-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-2-2-2-2-2-20020022-2-22200000000-2-222000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-22222-200200-2-2-2-2-2-2000000002222000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-222-2-2-2-2-2-2-2-2200-200-2-222220000000022-2-2000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-1-111111111-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111-222-2-2-2-1-11111-1-1-1-11111-1-111000000002-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111-2-2-2-222-1-111111111-1-1-1-1-1-11100000000-2211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-222-2221111-1-1-1-1-1-1-1-1-1-1111100000000-2-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-11111111111110000000022-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111112222-2-211-1-111-1-1-1-1111111-1-100000000-2211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111112-2-222211-1-1111111-1-1-1-111-1-1000000002-2-1-1110000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-1200-200-1-1-1-111−i3−i3i3i3−i3−i3i3i311110000000000−i3i3−i3i30000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-1200-200-1-1-1-111i3i3−i3−i3i3i3−i3−i311110000000000i3−i3i3−i30000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211111111-200200-1-111-1-1−i3−i3i3i3i3i3−i3−i311-1-10000000000−i3i3i3−i30000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211111111-200200-1-111-1-1i3i3−i3−i3−i3−i3i3i311-1-10000000000i3−i3−i3i30000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-200200111111−i3−i3i3i3−i3−i3i3i3-1-1-1-10000000000i3−i3i3−i30000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-200200111111i3i3−i3−i3i3i3−i3−i3-1-1-1-10000000000−i3i3−i3i30000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111200-20011-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-1110000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111200-20011-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-1110000000000−i3i3i3−i30000000000
χ372222-2-2-2-222-2-222-2-22-22-20000000022-2-2000000002i−2i00000000002i−2i2i−2i000022-2-20000000000002i−2i000000
χ382222-2-2-2-222-2-222-2-22-22-20000000022-2-2000000002i−2i00000000002i−2i2i−2i0000-2-222000000000000−2i2i000000
χ392222-2-2-2-222-2-222-2-22-22-20000000022-2-200000000−2i2i0000000000−2i2i−2i2i000022-2-2000000000000−2i2i000000
χ402222-2-2-2-222-2-222-2-22-22-20000000022-2-200000000−2i2i0000000000−2i2i−2i2i0000-2-2220000000000002i−2i000000
χ412-2-222-22-2222-2-2-2-22-2-22200002-22-22-22-222-2-200000000002-20000000000002i−2i2i−2i000000000000002i−2i0000
χ422-2-222-22-2222-2-2-2-22-2-22200002-22-22-22-222-2-200000000002-2000000000000−2i2i−2i2i00000000000000−2i2i0000
χ432-2-222-22-2222-2-2-2-22-2-2220000-22-222-22-2-2-2220000000000-220000000000002i−2i2i−2i00000000000000−2i2i0000
χ442-2-222-22-2222-2-2-2-22-2-2220000-22-222-22-2-2-2220000000000-22000000000000−2i2i−2i2i000000000000002i−2i0000
χ452-2-222-22-22-2-222-2-22-2-22200002-2-22-22-2222-2-20000000000-22000000000000000022-2-20000000000002-200
χ462-2-222-22-22-2-222-2-22-2-22200002-2-22-22-2222-2-20000000000-220000000000000000-2-222000000000000-2200
χ472-2-222-22-22-2-222-2-22-2-2220000-222-2-22-22-2-22200000000002-2000000000000000022-2-2000000000000-2200
χ482-2-222-22-22-2-222-2-22-2-2220000-222-2-22-22-2-22200000000002-20000000000000000-2-2220000000000002-200
χ492-2-22-22-2222-22-2-22-2-222-2000000002-2-22000002i−2i0000000002i−2i2i−2i000000002i−2i−2i2i00000000002-200000000
χ502-2-22-22-2222-22-2-22-2-222-2000000002-2-22000002i−2i0000000002i−2i2i−2i00000000−2i2i2i−2i0000000000-2200000000
χ512-2-22-22-2222-22-2-22-2-222-2000000002-2-2200000−2i2i000000000−2i2i−2i2i000000002i−2i−2i2i0000000000-2200000000
χ522-2-22-22-2222-22-2-22-2-222-2000000002-2-2200000−2i2i000000000−2i2i−2i2i00000000−2i2i2i−2i00000000002-200000000
χ534444-4-4-4-44-444-44-4-44-44-400000000-4-4440000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-24-4-44-222-22-2200000000-2-222000000004i−4i0000000000−2i2i−2i2i0000000000000000000000000000
χ554444-4-4-4-4-24-4-44-222-22-2200000000-2-22200000000−4i4i00000000002i−2i2i−2i0000000000000000000000000000
χ564444-4-4-4-4-2-444-4-222-22-220000000022-2-20000000000000000000023−23−23230000000000000000000000000000
χ574444-4-4-4-4-2-444-4-222-22-220000000022-2-200000000000000000000−232323−230000000000000000000000000000
χ5844-4-444-4-44000044-4-4-4-44004i−4i000000000000000000000000000000004i−4i00000000000000000000000000
χ5944-4-444-4-44000044-4-4-4-4400−4i4i00000000000000000000000000000000−4i4i00000000000000000000000000
χ6044-4-444-4-4-20000-2-22222-2004i−4i00000000−2i32i3−2i32i300000000000000000000−2i2i23−23000000000000000000000000
χ6144-4-444-4-4-20000-2-22222-2004i−4i000000002i3−2i32i3−2i300000000000000000000−2i2i−2323000000000000000000000000
χ6244-4-444-4-4-20000-2-22222-200−4i4i00000000−2i32i3−2i32i3000000000000000000002i−2i−2323000000000000000000000000
χ6344-4-444-4-4-20000-2-22222-200−4i4i000000002i3−2i32i3−2i3000000000000000000002i−2i23−23000000000000000000000000
χ6444-4-4-4-444400004-44-44-4-400000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ6544-4-4-4-444400004-44-44-4-4000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ664-44-44-4-4440000-4-4-444-444-4000000000000000000004-40000000000000000000000000000000000000000
χ674-44-44-4-4440000-4-4-444-44-4400000000000000000000-440000000000000000000000000000000000000000
χ684-44-44-4-44-20000222-2-22-24-40000000000−2i32i32i3−2i3000000-22−2i32i300000000000000000000000000000000000000
χ694-44-44-4-44-20000222-2-22-24-400000000002i3−2i3−2i32i3000000-222i3−2i300000000000000000000000000000000000000
χ704-44-44-4-44-20000222-2-22-2-440000000000−2i32i32i3−2i30000002-22i3−2i300000000000000000000000000000000000000
χ714-44-44-4-44-20000222-2-22-2-4400000000002i3−2i3−2i32i30000002-2−2i32i300000000000000000000000000000000000000
χ724-44-4-444-440000-4444-4-4-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ734-44-4-444-440000-4444-4-4-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ744-4-444-44-4-244-4-422-222-2-200004-44-4-22-22-2-2220000000000-22000000000000000000000000000000000000
χ754-4-444-44-4-244-4-422-222-2-20000-44-44-22-2222-2-200000000002-2000000000000000000000000000000000000
χ764-4-444-44-4-2-4-44422-222-2-200004-4-442-22-2-2-22200000000002-2000000000000000000000000000000000000
χ774-4-444-44-4-2-4-44422-222-2-20000-444-42-22-222-2-20000000000-22000000000000000000000000000000000000
χ784-4-44-44-444-44-44-44-4-444-400000000-444-40000000000000000000000000000000000000000000000000000
χ794-4-44-44-44-24-44-42-222-2-2200000000-222-2000004i−4i000000000−2i2i−2i2i00000000000000000000000000000000
χ804-4-44-44-44-24-44-42-222-2-2200000000-222-200000−4i4i0000000002i−2i2i−2i00000000000000000000000000000000
χ814-4-44-44-44-2-44-442-222-2-22000000002-2-22000000000000000023−23−232300000000000000000000000000000000
χ824-4-44-44-44-2-44-442-222-2-22000000002-2-220000000000000000−232323−2300000000000000000000000000000000
χ8388-8-8-8-888-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-888-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000

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