Finite Group Databasebeta

← Group #10858090

Character table — Group #10858090

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1
χ71111111111111111111111-1-1-1-111111111-1-11-1-11111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-11-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ911111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-111-1-1-11111-1-111-1
χ1011111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111-1-11
χ1111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111111-1-1-1-1-111-1-111-1-11
χ1211111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1-1111-1-111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11111-1-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111111-1-111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1-1-1-11111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-22222-200-20000000000-2-200000000000022-2-2-2-200000002000000000
χ18222222222-2-2-2-22222222220000-2-2-22222-200-20000000000-2-2000000000000-2-222220000000-2000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-20020000000000220000000000002222-2-20000000-2000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000000022000000000000-2-2-2-22200000002000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-21111-1-11111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22-2-222221111-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-22222-2-2111111-1-1-1-1-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-2-2-2-2-222111111-1-1-1-11111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-222-2-222-1-1-1-11111111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-2-2-222-2-2-1-1-1-1111111-1-1-1-111110000002-1-111000000000000
χ2922-222-2-2-2222-2-222-2-22-2-200000022-20000-22-2000000022-2-2000000000000002-2002-2000002-20000000000
χ3022-222-2-2-2222-2-222-2-22-2-200000022-20000-22-2000000022-2-200000000000000-2200-2200000-220000000000
χ3122-222-2-2-2222-2-222-2-22-2-200000022-20000-2-220000000-2-222000000000000002-2002-200000-220000000000
χ3222-222-2-2-2222-2-222-2-22-2-200000022-20000-2-220000000-2-22200000000000000-2200-22000002-20000000000
χ3322-222-2-2-22-2-22222-2-22-2-2002i2i−2i−2i-2-22000020000000000000002i2i−2i−2i000000002-200-22000000002i−2i0000000
χ3422-222-2-2-22-2-22222-2-22-2-2002i2i−2i−2i-2-22000020000000000000002i2i−2i−2i00000000-22002-200000000−2i2i0000000
χ3522-222-2-2-22-2-22222-2-22-2-200−2i−2i2i2i-2-2200002000000000000000−2i−2i2i2i000000002-200-2200000000−2i2i0000000
χ3622-222-2-2-22-2-22222-2-22-2-200−2i−2i2i2i-2-2200002000000000000000−2i−2i2i2i00000000-22002-2000000002i−2i0000000
χ372-222-22-2-222-2-22-2-2222-2-2002i−2i2i−2i2-2-2000020000000000000002i−2i2i−2i0000000000000000000000002i−2i002-20
χ382-222-22-2-222-2-22-2-2222-2-2002i−2i2i−2i2-2-2000020000000000000002i−2i2i−2i000000000000000000000000−2i2i00-220
χ392-222-22-2-222-2-22-2-2222-2-200−2i2i−2i2i2-2-200002000000000000000−2i2i−2i2i0000000000000000000000002i−2i00-220
χ402-222-22-2-222-2-22-2-2222-2-200−2i2i−2i2i2-2-200002000000000000000−2i2i−2i2i000000000000000000000000−2i2i002-20
χ412-2-22-2-2222-22-22-2-2-2-2222002-2-22-22-2000020002-22-2000000002-2-2222-2-200000000000002-2000000000000
χ422-2-22-2-2222-22-22-2-2-2-2222002-2-22-22-200002000-22-22000000002-2-22-2-2220000000000000-22000000000000
χ432-2-22-2-2222-22-22-2-2-2-222200-222-2-22-2000020002-2-2200000000-222-2-2-22200000000000002-2000000000000
χ442-2-22-2-2222-22-22-2-2-2-222200-222-2-22-200002000-222-200000000-222-222-2-20000000000000-22000000000000
χ452-2-22-2-222-1-22-221111-1-1-1002-2-221-11−i3−i3i3i3-10002-22-200−i3i3−i3i3−i3i3-111-1-1-111−i3−i3i3i30000000−i3i3-11000000000000
χ462-2-22-2-222-1-22-221111-1-1-1002-2-221-11−i3−i3i3i3-1000-22-2200−i3i3−i3i3−i3i3-111-111-1-1i3i3−i3−i30000000i3−i31-1000000000000
χ472-2-22-2-222-1-22-221111-1-1-1002-2-221-11i3i3−i3−i3-10002-22-200i3−i3i3−i3i3−i3-111-1-1-111i3i3−i3−i30000000i3−i3-11000000000000
χ482-2-22-2-222-1-22-221111-1-1-1002-2-221-11i3i3−i3−i3-1000-22-2200i3−i3i3−i3i3−i3-111-111-1-1−i3−i3i3i30000000−i3i31-1000000000000
χ492-2-22-2-222-1-22-221111-1-1-100-222-21-11−i3−i3i3i3-10002-2-2200i3−i3i3−i3−i3i31-1-1111-1-1i3i3−i3−i30000000−i3i3-11000000000000
χ502-2-22-2-222-1-22-221111-1-1-100-222-21-11−i3−i3i3i3-1000-222-200i3−i3i3−i3−i3i31-1-11-1-111−i3−i3i3i30000000i3−i31-1000000000000
χ512-2-22-2-222-1-22-221111-1-1-100-222-21-11i3i3−i3−i3-10002-2-2200−i3i3−i3i3i3−i31-1-1111-1-1−i3−i3i3i30000000i3−i3-11000000000000
χ522-2-22-2-222-1-22-221111-1-1-100-222-21-11i3i3−i3−i3-1000-222-200−i3i3−i3i3i3−i31-1-11-1-111i3i3−i3−i30000000−i3i31-1000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222-2-2-2-2200-400000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000222222220040000000000-2-200000000000000000000000000000000000
χ55444-4-4-44-4400004-44-4-44-40000000000000000000000000000000000000000000000000000000000022−22000
χ56444-4-4-44-4400004-44-4-44-400000000000000000000000000000000000000000000000000000000000−2222000
χ5744-444-4-4-4-244-4-4-2-222-222000000-2-22000024-40000000-2-2220000000000000000000000000000000000000
χ5844-444-4-4-4-244-4-4-2-222-222000000-2-2200002-44000000022-2-20000000000000000000000000000000000000
χ5944-444-4-4-4-2-4-444-2-222-222004i4i−4i−4i22-20000-2000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6044-444-4-4-4-2-4-444-2-222-22200−4i−4i4i4i22-20000-20000000000000002i2i−2i−2i0000000000000000000000000000000
χ6144-4-4-44-44400004-4-44-4-44000000000000000000000−2i22i200000000000000−2i22i2−2i22i200000000000000000000000
χ6244-4-4-44-44400004-4-44-4-440000000000000000000002i2−2i2000000000000002i2−2i22i2−2i200000000000000000000000
χ6344-4-4-44-44-20000-222-222-200000000023−2323−2300000000−2i22i20000000000i6−i6i6−i6i2−i2i2−i200000000000000000000000
χ6444-4-4-44-44-20000-222-222-200000000023−2323−23000000002i2−2i20000000000−i6i6−i6i6−i2i2−i2i200000000000000000000000
χ6544-4-4-44-44-20000-222-222-2000000000−2323−232300000000−2i22i20000000000−i6i6−i6i6i2−i2i2−i200000000000000000000000
χ6644-4-4-44-44-20000-222-222-2000000000−2323−2323000000002i2−2i20000000000i6−i6i6−i6−i2i2−i2i200000000000000000000000
χ674-444-44-4-44-444-4-4-4444-4-4000000-4440000-400000000000000000000000000000000000000000000000000
χ684-444-44-4-4-24-4-4422-2-2-222004i−4i4i−4i-2220000-2000000000000000−2i2i−2i2i0000000000000000000000000000000
χ694-444-44-4-4-24-4-4422-2-2-22200−4i4i−4i4i-2220000-20000000000000002i−2i2i−2i0000000000000000000000000000000
χ704-444-44-4-4-2-444-422-2-2-2220000002-2-200002000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ714-444-44-4-4-2-444-422-2-2-2220000002-2-2000020000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ724-44-44-4-4440000-444-4-4-444i−4i00000004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ734-44-44-4-4440000-444-4-4-44−4i4i0000000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ744-44-44-4-44-200002-2-2222-24i−4i0000000−2i2i2i−2i00000000000000000000i6−i6−i6i6−666−600000000000000000000000
χ754-44-44-4-44-200002-2-2222-24i−4i0000000−2i2i2i−2i00000000000000000000−i6i6i6−i66−6−6600000000000000000000000
χ764-44-44-4-44-200002-2-2222-2−4i4i00000002i−2i−2i2i00000000000000000000i6−i6−i6i66−6−6600000000000000000000000
χ774-44-44-4-44-200002-2-2222-2−4i4i00000002i−2i−2i2i00000000000000000000−i6i6i6−i6−666−600000000000000000000000
χ784-4-44-4-44444-44-4-4-4-4-44440000004-440000-400000000000000000000000000000000000000000000000000
χ794-4-44-4-444-24-44-42222-2-2-2000000-22-2−2i3−2i32i32i3200000000000002i3−2i300000000000000000000000000000000000
χ804-4-44-4-444-24-44-42222-2-2-2000000-22-22i32i3−2i3−2i320000000000000−2i32i300000000000000000000000000000000000
χ814-4-4-4444-440000-44-44-44-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ824-4-4-4444-440000-44-44-44-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ83888-8-8-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000

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