Finite Group Databasebeta

← Group #10844609

Character table — Group #10844609

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666644444444121212121212121244444412121212121212121212121212121212121244442466121244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-11111-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-1111111-1-1-1-1
χ911111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-11111-1-11111-1-1-1-11111-11-1-111-1-1-1-11111-1-111-1-1
χ1011111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-111-1-111
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-11-1-1-1-11111-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-1-111-1-111
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-111-1-11111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111
χ17222222222-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-20000-2-222-2-222-2-22200000000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2222222-2-2-2-20000-2222-2-2-2-222-2-200000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2222222-2-2-2-200002-2-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2000022-2-222-2-2222200000000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-21111-1-1-1-122-2-22-2-1-1-1-1111111-1-1-1-1111100002-2-1-11100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-21111-1-1-1-1-2-2222-2-1-1-1-11111111111-1-1-1-10000-2211-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-21111-1-1-1-122-2-2-221111-1-1-1-111-1-1-1-111110000-2211-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-21111-1-1-1-1-2-222-221111-1-1-1-1111111-1-1-1-100002-2-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-12222-2-211111111-1-1-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111-1-111111111000022-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-1222222-2-2111111110000-2-2-1-111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-1222222-2-2111111110000-2-2-1-111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111110000-22-1-11111-1-111−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111110000-22-1-11111-1-111i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1111100002-211-1-1-1-11111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1111100002-211-1-1-1-11111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-21111111100002211-1-111-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-21111111100002211-1-111-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i300000000000000
χ3722-2-222-2-222-2-2222-2-2-2-2200000000000022-2-22i−2i000000000000002i−2i2i−2i000022-2-20000000000002i−2i000000
χ3822-2-222-2-222-2-2222-2-2-2-2200000000000022-2-22i−2i000000000000002i−2i2i−2i0000-2-222000000000000−2i2i000000
χ3922-2-222-2-222-2-2222-2-2-2-2200000000000022-2-2−2i2i00000000000000−2i2i−2i2i000022-2-2000000000000−2i2i000000
χ4022-2-222-2-222-2-2222-2-2-2-2200000000000022-2-2−2i2i00000000000000−2i2i−2i2i0000-2-2220000000000002i−2i000000
χ412-22-22-22-222-22-2-2-2-222-220000000000002-22-2002-200000000000000002-22-22i−2i2i−2i0000000000000000002i−2i
χ422-22-22-22-222-22-2-2-2-222-220000000000002-22-2002-200000000000000002-22-2−2i2i−2i2i000000000000000000−2i2i
χ432-22-22-22-222-22-2-2-2-222-220000000000002-22-200-220000000000000000-22-222i−2i2i−2i000000000000000000−2i2i
χ442-22-22-22-222-22-2-2-2-222-220000000000002-22-200-220000000000000000-22-22−2i2i−2i2i0000000000000000002i−2i
χ452-2-222-2-22222-2-2-2-22-2-22200002-22-222-2-22-2-22000000000000002-2000000002i−2i−2i2i0000002i−2i000000000000
χ462-2-222-2-22222-2-2-2-22-2-22200002-22-222-2-22-2-22000000000000002-200000000−2i2i2i−2i000000−2i2i000000000000
χ472-2-222-2-22222-2-2-2-22-2-2220000-22-22-2-2222-2-2200000000000000-22000000002i−2i−2i2i000000−2i2i000000000000
χ482-2-222-2-22222-2-2-2-22-2-2220000-22-22-2-2222-2-2200000000000000-2200000000−2i2i2i−2i0000002i−2i000000000000
χ492-2-222-2-222-2-222-2-22-2-22200002-2-22-2-222-222-2000000000000002-2000000000000000000002-22-200000000
χ502-2-222-2-222-2-222-2-22-2-22200002-2-22-2-222-222-2000000000000002-200000000000000000000-22-2200000000
χ512-2-222-2-222-2-222-2-22-2-2220000-222-222-2-2-222-200000000000000-22000000000000000000002-2-2200000000
χ522-2-222-2-222-2-222-2-22-2-2220000-222-222-2-2-222-200000000000000-2200000000000000000000-222-200000000
χ534444-4-4-4-4400004-4-44-44-44-4000000000000000000004-40000000000000000000000000000000000000000
χ544444-4-4-4-4400004-4-44-44-4-4400000000000000000000-440000000000000000000000000000000000000000
χ554444-4-4-4-4-20000-222-22-224-400000023−2323−230000000000-22000023−230000000000000000000000000000000000
χ564444-4-4-4-4-20000-222-22-224-4000000−2323−23230000000000-220000−23230000000000000000000000000000000000
χ574444-4-4-4-4-20000-222-22-22-4400000023−2323−2300000000002-20000−23230000000000000000000000000000000000
χ584444-4-4-4-4-20000-222-22-22-44000000−2323−232300000000002-2000023−230000000000000000000000000000000000
χ5944-4-444-4-44-444-444-4-4-4-44000000000000-4-444000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-24-4-44-2-22222-2000000000000-2-2224i−4i00000000000000−2i2i−2i2i0000000000000000000000000000
χ6144-4-444-4-4-24-4-44-2-22222-2000000000000-2-222−4i4i000000000000002i−2i2i−2i0000000000000000000000000000
χ6244-4-444-4-4-2-444-4-2-22222-200000000000022-2-2000000000000000023−23−23230000000000000000000000000000
χ6344-4-444-4-4-2-444-4-2-22222-200000000000022-2-20000000000000000−232323−230000000000000000000000000000
χ6444-4-4-4-444400004-44-44-4-40000000000000000000000000000000000000000000000000000000000−2i22i20000
χ6544-4-4-4-444400004-44-44-4-400000000000000000000000000000000000000000000000000000000002i2−2i20000
χ664-44-44-44-44-44-44-4-4-444-44000000000000-44-44000000000000000000000000000000000000000000000000
χ674-44-44-44-4-24-44-4222-2-22-2000000000000-22-22004-40000000000000000-22-22000000000000000000000000
χ684-44-44-44-4-24-44-4222-2-22-2000000000000-22-2200-4400000000000000002-22-2000000000000000000000000
χ694-44-44-44-4-2-44-44222-2-22-20000000000002-22-200000000000000000000−2i32i32i3−2i3000000000000000000000000
χ704-44-44-44-4-2-44-44222-2-22-20000000000002-22-2000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ714-44-4-44-4440000-4444-4-4-4000000000000000000000000000000000000000000000000000000000000−2i22i200
χ724-44-4-44-4440000-4444-4-4-40000000000000000000000000000000000000000000000000000000000002i2−2i200
χ734-4-444-4-44-244-4-422-222-2-200004-44-4-2-222-222-200000000000000-2200000000000000000000000000000000
χ744-4-444-4-44-244-4-422-222-2-20000-44-4422-2-2-222-2000000000000002-200000000000000000000000000000000
χ754-4-444-4-44-2-4-44422-222-2-200004-4-4422-2-22-2-2200000000000000-2200000000000000000000000000000000
χ764-4-444-4-44-2-4-44422-222-2-20000-444-4-2-2222-2-22000000000000002-200000000000000000000000000000000
χ774-4-44-444-440000-44-4-444-4004i−4i00000000000000000000004i−4i000000000000000000000000000000000000
χ784-4-44-444-440000-44-4-444-400−4i4i0000000000000000000000−4i4i000000000000000000000000000000000000
χ794-4-44-444-4-200002-222-2-22004i−4i000023−23−2323000000000000−2i32i3−2i2i000000000000000000000000000000000000
χ804-4-44-444-4-200002-222-2-22004i−4i0000−232323−230000000000002i3−2i3−2i2i000000000000000000000000000000000000
χ814-4-44-444-4-200002-222-2-2200−4i4i000023−23−23230000000000002i3−2i32i−2i000000000000000000000000000000000000
χ824-4-44-444-4-200002-222-2-2200−4i4i0000−232323−23000000000000−2i32i32i−2i000000000000000000000000000000000000
χ8388-8-8-8-888-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000

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