Finite Group Databasebeta

← Group #10845264

Character table — Group #10845264

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order122222223444466666664444444412121212121212124444441212121212121212121212121212121212124444441212121222444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-111111111-111-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-111111111-111-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1
χ911111111111111111111-1-111-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-1-11111-1-1
χ1011111111111111111111-1-111-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11111-1-111-1-1-1-111
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-1-1-11111-1-1-1-111
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-11-1-11111-1-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-1111111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-1-111111-111-1-111-1-1-1-111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-111-1-111
χ17222222222-2-2-2-222222222222-2-2-2-22222-2-2-2-2200-20022-2-222-2-20000-2-20000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2222222-2-2-2-2-200200-2-222-2-2220000-2-20000000000000000000000000000
χ19222222222-2-2-2-22222222-2-2222222-2-2-2-2-2-2-2-2-200-20022-2-2-2-2220000220000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2200200-2-22222-2-20000220000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-1-1-1-11111-1-111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-222-22211111111-1-1-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111-1-11111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-21111-1-1-1-1-2222-2-2-1-1-1-11111111111-1-1-1-100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-21111-1-1-1-1-2-2-2222-1-1-1-11111-1-1-1-11111110000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2221111-1-1-1-1222-2-2-21111-1-1-1-1111111-1-1-1-10000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2221111-1-1-1-12-2-2-2221111-1-1-1-1-1-1-1-111111100002-2-1-11100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111200-200-1-111-1-111−i3−i3i3i311−i3−i3i3i3000000−i3i3−i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111200-200-1-111-1-111i3i3−i3−i311i3i3−i3−i3000000i3−i3i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-11111-20020011-1-111-1-1−i3−i3i3i311−i3−i3i3i3000000i3−i3i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-11111-20020011-1-111-1-1i3i3−i3−i311i3i3−i3−i3000000−i3i3−i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222222211111111-200-200-1-11111-1-1−i3−i3i3i3-1-1i3i3−i3−i3000000i3−i3−i3i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222222211111111-200-200-1-11111-1-1i3i3−i3−i3-1-1−i3−i3i3i3000000−i3i3i3−i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-21111111120020011-1-1-1-111−i3−i3i3i3-1-1i3i3−i3−i3000000−i3i3i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-21111111120020011-1-1-1-111i3i3−i3−i3-1-1−i3−i3i3i3000000i3−i3−i3i300000000000000
χ3722-2-22-2-2222-2-2222-2-2-22-200000000000022-2-200002-2000000002-22-20000002i2i−2i−2i0000000000002i−2i000000
χ3822-2-22-2-2222-2-2222-2-2-22-200000000000022-2-200002-2000000002-22-2000000−2i−2i2i2i000000000000−2i2i000000
χ3922-2-22-2-2222-2-2222-2-2-22-200000000000022-2-20000-2200000000-22-220000002i2i−2i−2i000000000000−2i2i000000
χ4022-2-22-2-2222-2-2222-2-2-22-200000000000022-2-20000-2200000000-22-22000000−2i−2i2i2i0000000000002i−2i000000
χ412-22-2-22-22222-2-2-2-22-2-2222-2002-20022-2-22-22-20000000000000000002-200002i−2i2i−2i000000002i−2i0000000000
χ422-22-2-22-22222-2-2-2-22-2-2222-2002-20022-2-22-22-20000000000000000002-20000−2i2i−2i2i00000000−2i2i0000000000
χ432-22-2-22-22222-2-2-2-22-2-222-2200-2200-2-2222-22-2000000000000000000-2200002i−2i2i−2i00000000−2i2i0000000000
χ442-22-2-22-22222-2-2-2-22-2-222-2200-2200-2-2222-22-2000000000000000000-220000−2i2i−2i2i000000002i−2i0000000000
χ452-22-2-22-222-2-222-2-22-2-2222-200-220022-2-2-22-22000000000000000000-22000000000000002-2002-200000000
χ462-22-2-22-222-2-222-2-22-2-2222-200-220022-2-2-22-22000000000000000000-2200000000000000-2200-2200000000
χ472-22-2-22-222-2-222-2-22-2-222-22002-200-2-222-22-220000000000000000002-2000000000000002-200-2200000000
χ482-22-2-22-222-2-222-2-22-2-222-22002-200-2-222-22-220000000000000000002-200000000000000-22002-200000000
χ492-2-22-2-22222-22-2-2-2-2222-20000000000002-2-2202i−2i000000000000000002i−2i2i−2i2-2-22000000000000002i−2i0000
χ502-2-22-2-22222-22-2-2-2-2222-20000000000002-2-2202i−2i000000000000000002i−2i2i−2i-222-200000000000000−2i2i0000
χ512-2-22-2-22222-22-2-2-2-2222-20000000000002-2-220−2i2i00000000000000000−2i2i−2i2i2-2-2200000000000000−2i2i0000
χ522-2-22-2-22222-22-2-2-2-2222-20000000000002-2-220−2i2i00000000000000000−2i2i−2i2i-222-2000000000000002i−2i0000
χ53444-4-4-44-4400004-444-4-4-40000004-4000000000000000000004-40000000000000000000000000000000000
χ54444-4-4-44-4400004-444-4-4-4000000-4400000000000000000000-440000000000000000000000000000000000
χ55444-4-4-44-4-20000-22-2-22220000004-4−2i32i3−2i32i3000000000000−2i32i300-220000000000000000000000000000000000
χ56444-4-4-44-4-20000-22-2-22220000004-42i3−2i32i3−2i30000000000002i3−2i300-220000000000000000000000000000000000
χ57444-4-4-44-4-20000-22-2-2222000000-44−2i32i3−2i32i30000000000002i3−2i3002-20000000000000000000000000000000000
χ58444-4-4-44-4-20000-22-2-2222000000-442i3−2i32i3−2i3000000000000−2i32i3002-20000000000000000000000000000000000
χ5944-44-44-4-4400004-4-4-44-44000000000000000000000000000000000000000000000000000000000000−2i22i200
χ6044-44-44-4-4400004-4-4-44-440000000000000000000000000000000000000000000000000000000000002i2−2i200
χ6144-4-44-4-444-444-444-4-4-44-4000000000000-4-444000000000000000000000000000000000000000000000000
χ6244-4-44-4-44-24-4-44-2-2222-22000000000000-2-22200004-400000000-22-22000000000000000000000000000000
χ6344-4-44-4-44-24-4-44-2-2222-22000000000000-2-2220000-44000000002-22-2000000000000000000000000000000
χ6444-4-44-4-44-2-444-4-2-2222-2200000000000022-2-200000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6544-4-44-4-44-2-444-4-2-2222-2200000000000022-2-2000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ664-4444-4-4-440000-444-44-4-4004-40000000000000000004-40000000000000000000000000000000000000000
χ674-4444-4-4-440000-444-44-4-400-44000000000000000000-440000000000000000000000000000000000000000
χ684-4444-4-4-4-200002-2-22-222004-40000−2i32i32i3−2i30000000000-2200−2i32i3000000000000000000000000000000000000
χ694-4444-4-4-4-200002-2-22-222004-400002i3−2i3−2i32i30000000000-22002i3−2i3000000000000000000000000000000000000
χ704-4444-4-4-4-200002-2-22-22200-440000−2i32i32i3−2i300000000002-2002i3−2i3000000000000000000000000000000000000
χ714-4444-4-4-4-200002-2-22-22200-4400002i3−2i3−2i32i300000000002-200−2i32i3000000000000000000000000000000000000
χ724-44-4-44-44-244-4-422-222-2-24-4004-400-2-222-22-22000000000000000000-220000000000000000000000000000
χ734-44-4-44-44-244-4-422-222-2-2-4400-440022-2-2-22-220000000000000000002-20000000000000000000000000000
χ744-44-4-44-44-2-4-44422-222-2-24-400-4400-2-2222-22-20000000000000000002-20000000000000000000000000000
χ754-44-4-44-44-2-4-44422-222-2-2-44004-40022-2-22-22-2000000000000000000-220000000000000000000000000000
χ764-4-44-4-4444-44-44-4-4-4444-4000000000000-444-4000000000000000000000000000000000000000000000000
χ774-4-44-4-444-24-44-4222-2-2-22000000000000-222-204i−4i00000000000000000−2i2i−2i2i000000000000000000000000
χ784-4-44-4-444-24-44-4222-2-2-22000000000000-222-20−4i4i000000000000000002i−2i2i−2i000000000000000000000000
χ794-4-44-4-444-2-44-44222-2-2-220000000000002-2-220000000000000000000023−23−2323000000000000000000000000
χ804-4-44-4-444-2-44-44222-2-2-220000000000002-2-2200000000000000000000−232323−23000000000000000000000000
χ814-4-4-4444-440000-44-44-4-440000000000000000000000000000000000000000000000000000000000000022−22
χ824-4-4-4444-440000-44-44-4-4400000000000000000000000000000000000000000000000000000000000000−2222
χ8388-88-88-8-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000

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