Finite Group Databasebeta

← Group #10831708

Character table — Group #10831708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order12222222344446666666444444441212121212121212224444666612121212121212121212121212122222441212121244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-111-1-11111-1-1-1-1111-1-1-11111-1-111-1-111-1-1-1-1-1-111111-111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111-1-11111-1-1-1-1111-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1-111-1-111-1-111111111-11-1-111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-11-1-11111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111-11-1-11111-1-1-1-111-1-111-1-1-1-11111-11-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-11-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-111111111111-111-1-1-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-111-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-222-2-2-2-2-2-2222200-22000000-2-222-2-2-2-2220000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-22222002-2000000-2-2-2-22222-2-20000000000000000000000000000
χ19222222222-2-2-2-22222222-2-2222222-2-2-2-2-2-2-2-200-2-2000000222222-2-2-2-20000000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2002200000022-2-2-2-222220000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1-1-1-1-1-1-111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-122-2-222-1-1-1-1-1-111111111-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-11111222-2-2-2-1-1-1-111-1-111-1-111111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-11111-2-22-222111111-1-111-1-111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-1111122-22-2-2-1-1-1-11111-1-111-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-11111-2-2-222211111111-1-111-1-1-1-1-1-100002-2-1-11100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-100-2200−i3−i3i3i311-1-11111-1-1−i3−i3i3i3000000−i3i3−i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-100-2200i3i3−i3−i311-1-11111-1-1i3i3−i3−i3000000i3−i3i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-1002-200−i3−i3i3i31111-1-1-1-111−i3−i3i3i3000000i3−i3i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-1002-200i3i3−i3−i31111-1-1-1-111i3i3−i3−i3000000−i3i3−i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222221111111100-2-200−i3−i3i3i3-1-1-1-1-1-11111i3i3−i3−i3000000−i3i3i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222221111111100-2-200i3i3−i3−i3-1-1-1-1-1-11111−i3−i3i3i3000000i3−i3−i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-211111111002200−i3−i3i3i3-1-11111-1-1-1-1i3i3−i3−i3000000i3−i3−i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-211111111002200i3i3−i3−i3-1-11111-1-1-1-1−i3−i3i3i3000000−i3i3i3−i300000000000000
χ372222-2-2-2-2222-2-2222-2-2-2-20000000022-2-200002-200002-22-20000000000000022-2-20000000000002-2000000
χ382222-2-2-2-2222-2-2222-2-2-2-20000000022-2-200002-200002-22-200000000000000-2-222000000000000-22000000
χ392222-2-2-2-2222-2-2222-2-2-2-20000000022-2-20000-220000-22-220000000000000022-2-2000000000000-22000000
χ402222-2-2-2-2222-2-2222-2-2-2-20000000022-2-20000-220000-22-2200000000000000-2-2220000000000002-2000000
χ412-2-2222-2-22-22-22-2-2222-2-2000000002-22-2000000002i−2i000000000000002i−2i2i−2i2-22-2000000000000002i−2i0000
χ422-2-2222-2-22-22-22-2-2222-2-2000000002-22-2000000002i−2i000000000000002i−2i2i−2i-22-2200000000000000−2i2i0000
χ432-2-2222-2-22-22-22-2-2222-2-2000000002-22-200000000−2i2i00000000000000−2i2i−2i2i2-22-200000000000000−2i2i0000
χ442-2-2222-2-22-22-22-2-2222-2-2000000002-22-200000000−2i2i00000000000000−2i2i−2i2i-22-22000000000000002i−2i0000
χ452-2-22-2-22222-2-22-2-22-2-2222-22-20000-222-222-2-200000000002-20000000000000000000000002-22-200000000
χ462-2-22-2-22222-2-22-2-22-2-2222-22-20000-222-222-2-200000000002-2000000000000000000000000-22-2200000000
χ472-2-22-2-22222-2-22-2-22-2-222-22-220000-222-2-2-2220000000000-220000000000000000000000002-2-2200000000
χ482-2-22-2-22222-2-22-2-22-2-222-22-220000-222-2-2-2220000000000-22000000000000000000000000-222-200000000
χ492-2-22-2-2222-222-2-2-22-2-2222-2-2200002-2-2222-2-20000000000-220000000000002-2-220000002-2000000000000
χ502-2-22-2-2222-222-2-2-22-2-2222-2-2200002-2-2222-2-20000000000-22000000000000-222-2000000-22000000000000
χ512-2-22-2-2222-222-2-2-22-2-222-222-200002-2-22-2-22200000000002-20000000000002-2-22000000-22000000000000
χ522-2-22-2-2222-222-2-2-22-2-222-222-200002-2-22-2-22200000000002-2000000000000-222-20000002-2000000000000
χ534444-4-4-4-44-4-444444-4-4-4-400000000-4-4440000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-244-4-4-2-2-2222200000000-2-22200004-40000-22-2200000000000000000000000000000000000000
χ554444-4-4-4-4-244-4-4-2-2-2222200000000-2-2220000-4400002-22-200000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-444-2-2-222220000000022-2-20000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ574444-4-4-4-4-2-4-444-2-2-222220000000022-2-200000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ5844-4-44-44-4400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ5944-4-44-44-4400004-4-44-4-44000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ6044-4-4-44-44400004-4-4-444-40000004-400000000000000000000004-400000000000000000000000000000000
χ6144-4-4-44-44400004-4-4-444-4000000-440000000000000000000000-4400000000000000000000000000000000
χ6244-4-4-44-44-20000-2222-2-220000004-4000023−2323−2300000000000000-2223−23000000000000000000000000000000
χ6344-4-4-44-44-20000-2222-2-220000004-40000−2323−232300000000000000-22−2323000000000000000000000000000000
χ6444-4-4-44-44-20000-2222-2-22000000-44000023−2323−23000000000000002-2−2323000000000000000000000000000000
χ6544-4-4-44-44-20000-2222-2-22000000-440000−2323−2323000000000000002-223−23000000000000000000000000000000
χ664-44-44-4-4440000-44-44-44-400004-400000000000000000000004-40000000000000000000000000000000000
χ674-44-44-4-4440000-44-44-44-40000-440000000000000000000000-440000000000000000000000000000000000
χ684-44-44-4-44-200002-22-22-2200004-400000023−23−2323000000000000-22000023−230000000000000000000000000000
χ694-44-44-4-44-200002-22-22-2200004-4000000−232323−23000000000000-220000−23230000000000000000000000000000
χ704-44-44-4-44-200002-22-22-220000-4400000023−23−23230000000000002-20000−23230000000000000000000000000000
χ714-44-44-4-44-200002-22-22-220000-44000000−232323−230000000000002-2000023−230000000000000000000000000000
χ724-44-4-444-440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000−2i22i200
χ734-44-4-444-440000-44-4-44-440000000000000000000000000000000000000000000000000000000000002i2−2i200
χ744-4-4444-4-444-44-4-4-4444-4-400000000-44-440000000000000000000000000000000000000000000000000000
χ754-4-4444-4-4-24-44-422-2-2-222000000002-22-200000000000000000000000023−23−2323000000000000000000000000
χ764-4-4444-4-4-24-44-422-2-2-222000000002-22-2000000000000000000000000−232323−23000000000000000000000000
χ774-4-4444-4-4-2-44-4422-2-2-22200000000-22-22000000004i−4i00000000000000−2i2i−2i2i000000000000000000000000
χ784-4-4444-4-4-2-44-4422-2-2-22200000000-22-2200000000−4i4i000000000000002i−2i2i−2i000000000000000000000000
χ794-4-44-4-444-24-4-4422-222-2-24-44-400002-2-22-2-2220000000000-22000000000000000000000000000000000000
χ804-4-44-4-444-24-4-4422-222-2-2-44-4400002-2-2222-2-200000000002-2000000000000000000000000000000000000
χ814-4-44-4-444-2-444-422-222-2-24-4-440000-222-2-2-22200000000002-2000000000000000000000000000000000000
χ824-4-44-4-444-2-444-422-222-2-2-444-40000-222-222-2-20000000000-22000000000000000000000000000000000000
χ8388-8-88-88-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-888-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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