Finite Group Databasebeta

← Group #10846105

Character table — Group #10846105

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344446666666224444441212121212121212244444666612121212121212121212121212128888888844121212124444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111-1-1-1-111-1-1-1-11111-111-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111111-111-1-111-1-1-1-1-1-11-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-111-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1111111-11
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-11-1-111-1-111-1-1-1-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-111111-1
χ911111111111111111111-1-11111-1-111111111-111-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ1011111111111111111111-1-11111-1-111111111-111-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ1211111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111-1-11111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-111-1-1-1-111-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111-111-1-111-1-111-1-1-11
χ17222222222-2-2-2-222222222222-2-2-2-22222-2-2-2-2200-2002222-2-20000-2-2-2-20000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-2-2-20020022-2-2220000-2-2220000000000000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2222222-2-2-2-2-200200-2-2-2-2-2-2000022220000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-2200-200-2-22222000022-2-20000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-1-11111-1-1-1-1111100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-1-222-2-2-2-1-11111-1-1-1-1-1-1111111000000002-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-1-2-2-2-222-1-111111111-1-111-1-1-1-100000000-2211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-222-2221111-1-1-1-1-1-11111-1-1-1-100000000-2-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-11111111111110000000022-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-12222-2-211-1-111-1-1-1-111-1-1111100000000-2211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-12-2-222211-1-111111111-1-1-1-1-1-1000000002-2-1-1110000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111200-200-1-1-1-111−i3−i3i3i31111−i3−i3i3i30000000000−i3i3−i3i30000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111200-200-1-1-1-111i3i3−i3−i31111i3i3−i3−i30000000000i3−i3i3−i30000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211111111-200200-1-111-1-1−i3−i3i3i311-1-1i3i3−i3−i30000000000−i3i3i3−i30000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211111111-200200-1-111-1-1i3i3−i3−i311-1-1−i3−i3i3i30000000000i3−i3−i3i30000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-1-1-11111-200200111111−i3−i3i3i3-1-1-1-1−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-1-1-11111-200200111111i3i3−i3−i3-1-1-1-1i3i3−i3−i30000000000−i3i3−i3i30000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111200-20011-1-1-1-1−i3−i3i3i3-1-111i3i3−i3−i30000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111200-20011-1-1-1-1i3i3−i3−i3-1-111−i3−i3i3i30000000000−i3i3i3−i30000000000
χ3722-2-2-22-2222-22-222-2-2-2-2200000000000022-2-202i−2i0000000002i−2i2i−2i000000002i2i−2i−2i00000000002-200000000
χ3822-2-2-22-2222-22-222-2-2-2-2200000000000022-2-202i−2i0000000002i−2i2i−2i00000000−2i−2i2i2i0000000000-2200000000
χ3922-2-2-22-2222-22-222-2-2-2-2200000000000022-2-20−2i2i000000000−2i2i−2i2i000000002i2i−2i−2i0000000000-2200000000
χ4022-2-2-22-2222-22-222-2-2-2-2200000000000022-2-20−2i2i000000000−2i2i−2i2i00000000−2i−2i2i2i00000000002-200000000
χ412-22-2-2-22222-2-22-2-22-2-2220000000000002-22-200002-2000000000000002-22-22-22-20000000000002-2000000
χ422-22-2-2-22222-2-22-2-22-2-2220000000000002-22-200002-2000000000000002-22-2-22-22000000000000-22000000
χ432-22-2-2-22222-2-22-2-22-2-2220000000000002-22-20000-2200000000000000-22-222-22-2000000000000-22000000
χ442-22-2-2-22222-2-22-2-22-2-2220000000000002-22-20000-2200000000000000-22-22-22-220000000000002-2000000
χ452-2-222-2-22222-2-2-2-2-222-22002-22-20022-2-22-2-2200000000002-20000000000002i−2i−2i2i000000000000002i−2i0000
χ462-2-222-2-22222-2-2-2-2-222-22002-22-20022-2-22-2-2200000000002-2000000000000−2i2i2i−2i00000000000000−2i2i0000
χ472-2-222-2-22222-2-2-2-2-222-2200-22-2200-2-2222-2-220000000000-220000000000002i−2i−2i2i00000000000000−2i2i0000
χ482-2-222-2-22222-2-2-2-2-222-2200-22-2200-2-2222-2-220000000000-22000000000000−2i2i2i−2i000000000000002i−2i0000
χ492-2-222-2-222-2-222-2-2-222-22002-2-220022-2-2-222-20000000000-22000000000000000022-2-20000000000002-200
χ502-2-222-2-222-2-222-2-2-222-22002-2-220022-2-2-222-20000000000-220000000000000000-2-222000000000000-2200
χ512-2-222-2-222-2-222-2-2-222-2200-222-200-2-222-222-200000000002-2000000000000000022-2-2000000000000-2200
χ522-2-222-2-222-2-222-2-2-222-2200-222-200-2-222-222-200000000002-20000000000000000-2-2220000000000002-200
χ53444-44-4-4-4400004-44-44-4-40000000000000000000000000000000000000000000022−2222−220000000000000000
χ54444-44-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000−2222−22220000000000000000
χ5544-44-4-44-4400004-4-44-44-40000004i−4i0000000000000000000000004i−4i000000000000000000000000000000
χ5644-44-4-44-4400004-4-44-44-4000000−4i4i000000000000000000000000−4i4i000000000000000000000000000000
χ5744-44-4-44-4-20000-222-22-220000004i−4i−2i32i3−2i32i300000000000000000000−2i2i23−230000000000000000000000000000
χ5844-44-4-44-4-20000-222-22-220000004i−4i2i3−2i32i3−2i300000000000000000000−2i2i−23230000000000000000000000000000
χ5944-44-4-44-4-20000-222-22-22000000−4i4i−2i32i3−2i32i3000000000000000000002i−2i−23230000000000000000000000000000
χ6044-44-4-44-4-20000-222-22-22000000−4i4i2i3−2i32i3−2i3000000000000000000002i−2i23−230000000000000000000000000000
χ6144-4-4-44-444-44-4444-4-4-4-44000000000000-4-444000000000000000000000000000000000000000000000000
χ6244-4-4-44-44-24-44-4-2-22222-2000000000000-2-22204i−4i000000000−2i2i−2i2i00000000000000000000000000000000
χ6344-4-4-44-44-24-44-4-2-22222-2000000000000-2-2220−4i4i0000000002i−2i2i−2i00000000000000000000000000000000
χ6444-4-4-44-44-2-44-44-2-22222-200000000000022-2-200000000000023−23−232300000000000000000000000000000000
χ6544-4-4-44-44-2-44-44-2-22222-200000000000022-2-2000000000000−232323−2300000000000000000000000000000000
χ664-444-44-4-440000-4444-4-4-44-4000000000000000000004-40000000000000000000000000000000000000000
χ674-444-44-4-440000-4444-4-4-4-4400000000000000000000-440000000000000000000000000000000000000000
χ684-444-44-4-4-200002-2-2-22224-4000000−2i32i32i3−2i30000000000-22−2i32i300000000000000000000000000000000000000
χ694-444-44-4-4-200002-2-2-22224-40000002i3−2i3−2i32i30000000000-222i3−2i300000000000000000000000000000000000000
χ704-444-44-4-4-200002-2-2-2222-44000000−2i32i32i3−2i300000000002-22i3−2i300000000000000000000000000000000000000
χ714-444-44-4-4-200002-2-2-2222-440000002i3−2i3−2i32i300000000002-2−2i32i300000000000000000000000000000000000000
χ724-44-4-4-4444-444-4-4-44-4-444000000000000-44-44000000000000000000000000000000000000000000000000
χ734-44-4-4-444-24-4-4422-222-2-2000000000000-22-2200004-400000000000000-22-22000000000000000000000000
χ744-44-4-4-444-24-4-4422-222-2-2000000000000-22-220000-44000000000000002-22-2000000000000000000000000
χ754-44-4-4-444-2-444-422-222-2-20000000000002-22-200000000000000000000−2i32i32i3−2i3000000000000000000000000
χ764-44-4-4-444-2-444-422-222-2-20000000000002-22-2000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ774-4-444-4-44-244-4-4222-2-22-2004-44-400-2-222-222-20000000000-22000000000000000000000000000000000000
χ784-4-444-4-44-244-4-4222-2-22-200-44-440022-2-2-222-200000000002-2000000000000000000000000000000000000
χ794-4-444-4-44-2-4-444222-2-22-2004-4-4400-2-2222-2-2200000000002-2000000000000000000000000000000000000
χ804-4-444-4-44-2-4-444222-2-22-200-444-40022-2-22-2-220000000000-22000000000000000000000000000000000000
χ814-4-4-4444-440000-44-4-444-40000000000000000000000000000000000000000000022−22−22220000000000000000
χ824-4-4-4444-440000-44-4-444-400000000000000000000000000000000000000000000−222222−220000000000000000
χ83888-88-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

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