Finite Group Databasebeta

← Group #10868269

Character table — Group #10868269

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424444444412121212244444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ51111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-111-1-11111-1-1-1
χ1011111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-11-1-111-1-1-1-1111
χ1111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-1-1-111-1-1111
χ1211111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-11111111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-11111-1-1-1-111-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-11-1-1-1-11111-1-11
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111111-1-111-1-111-1
χ17222222222-2-2-2-22222222220000-2-2-22222-2-200000000-2-200000000000000002222-2-200000-200000000000
χ18222222222-2-2-2-22222222220000-2-2-22222-2-200000000-2-20000000000000000-2-2-2-22200000200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000000022000000000000000022-2-2-2-200000200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-2222200000-200000000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-22222-2-211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-22222-2-222111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-222-2-222-2-2111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ2922-22-2-22-2222-2-22-22-2-2-220000002-2-20000202-200000000000022-2-2000000002i−2i002i−2i000000002i−2i0000000
χ3022-22-2-22-2222-2-22-22-2-2-220000002-2-20000202-200000000000022-2-200000000−2i2i00−2i2i00000000−2i2i0000000
χ3122-22-2-22-2222-2-22-22-2-2-220000002-2-2000020-22000000000000-2-222000000002i−2i002i−2i00000000−2i2i0000000
χ3222-22-2-22-2222-2-22-22-2-2-220000002-2-2000020-22000000000000-2-22200000000−2i2i00−2i2i000000002i−2i0000000
χ3322-22-2-22-22-2-2222-22-2-2-22002i2i−2i−2i-2220000-2000000000002i2i−2i−2i0000000000002i−2i00−2i2i00000000002-200000
χ3422-22-2-22-22-2-2222-22-2-2-22002i2i−2i−2i-2220000-2000000000002i2i−2i−2i000000000000−2i2i002i−2i0000000000-2200000
χ3522-22-2-22-22-2-2222-22-2-2-2200−2i−2i2i2i-2220000-200000000000−2i−2i2i2i0000000000002i−2i00−2i2i0000000000-2200000
χ3622-22-2-22-22-2-2222-22-2-2-2200−2i−2i2i2i-2220000-200000000000−2i−2i2i2i000000000000−2i2i002i−2i00000000002-200000
χ372-22-22-22-22-222-2-2-2222-2-2002i−2i2i−2i-22-2000020002i−2i2-200002i−2i2i−2i000022-2-2000000000002i−2i00000000000000
χ382-22-22-22-22-222-2-2-2222-2-2002i−2i2i−2i-22-200002000−2i2i-2200002i−2i2i−2i0000-2-22200000000000−2i2i00000000000000
χ392-22-22-22-22-222-2-2-2222-2-200−2i2i−2i2i-22-2000020002i−2i-220000−2i2i−2i2i0000-2-222000000000002i−2i00000000000000
χ402-22-22-22-22-222-2-2-2222-2-200−2i2i−2i2i-22-200002000−2i2i2-20000−2i2i−2i2i000022-2-200000000000−2i2i00000000000000
χ412-22-22-22-2-1-222-211-1-1-111002i−2i2i−2i1-11−i3−i3i3i3-10002i−2i2-200−i3i3−ii−ii3−33−3-1-111−i3−i3i3i30000000−ii3−3000000000000
χ422-22-22-22-2-1-222-211-1-1-111002i−2i2i−2i1-11−i3−i3i3i3-1000−2i2i-2200−i3i3−ii−ii3−33−311-1-1i3i3−i3−i30000000i−i−33000000000000
χ432-22-22-22-2-1-222-211-1-1-111002i−2i2i−2i1-11i3i3−i3−i3-10002i−2i2-200i3−i3−ii−ii−33−33-1-111i3i3−i3−i30000000−ii−33000000000000
χ442-22-22-22-2-1-222-211-1-1-111002i−2i2i−2i1-11i3i3−i3−i3-1000−2i2i-2200i3−i3−ii−ii−33−3311-1-1−i3−i3i3i30000000i−i3−3000000000000
χ452-22-22-22-2-1-222-211-1-1-11100−2i2i−2i2i1-11−i3−i3i3i3-10002i−2i-2200−i3i3i−ii−i−33−3311-1-1i3i3−i3−i30000000−ii3−3000000000000
χ462-22-22-22-2-1-222-211-1-1-11100−2i2i−2i2i1-11−i3−i3i3i3-1000−2i2i2-200−i3i3i−ii−i−33−33-1-111−i3−i3i3i30000000i−i−33000000000000
χ472-22-22-22-2-1-222-211-1-1-11100−2i2i−2i2i1-11i3i3−i3−i3-10002i−2i-2200i3−i3i−ii−i3−33−311-1-1−i3−i3i3i30000000−ii−33000000000000
χ482-22-22-22-2-1-222-211-1-1-11100−2i2i−2i2i1-11i3i3−i3−i3-1000−2i2i2-200i3−i3i−ii−i3−33−3-1-111i3i3−i3−i30000000i−i3−3000000000000
χ492-2-2-2-222222-22-2-222-2-22-2002-2-2222-20000-2000000000002-2-220000000000000000000000002i−2i00002i−2i000
χ502-2-2-2-222222-22-2-222-2-22-2002-2-2222-20000-2000000000002-2-22000000000000000000000000−2i2i0000−2i2i000
χ512-2-2-2-222222-22-2-222-2-22-200-222-222-20000-200000000000-222-20000000000000000000000002i−2i0000−2i2i000
χ522-2-2-2-222222-22-2-222-2-22-200-222-222-20000-200000000000-222-2000000000000000000000000−2i2i00002i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222-2-2-2-22-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-4-4-44400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000022−220
χ56444-4-4-4-44400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000−22220
χ5744-44-4-44-4-244-4-4-22-2222-2000000-2220000-204-4000000000000-2-2220000000000000000000000000000000
χ5844-44-4-44-4-244-4-4-22-2222-2000000-2220000-20-4400000000000022-2-20000000000000000000000000000000
χ5944-44-4-44-4-2-4-444-22-2222-2004i4i−4i−4i2-2-20000200000000000−2i−2i2i2i00000000000000000000000000000000000
χ6044-44-4-44-4-2-4-444-22-2222-200−4i−4i4i4i2-2-200002000000000002i2i−2i−2i00000000000000000000000000000000000
χ6144-4-444-4-44000044-4-44-4-400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ6244-4-444-4-44000044-4-44-4-4000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ6344-4-444-4-4-20000-2-222-222000000000−2i32i3−2i32i30000000022−220000000000i6−i6i6−i6−22−2200000000000000000000000
χ6444-4-444-4-4-20000-2-222-222000000000−2i32i3−2i32i300000000−22220000000000−i6i6−i6i62−22−200000000000000000000000
χ6544-4-444-4-4-20000-2-222-2220000000002i3−2i32i3−2i30000000022−220000000000−i6i6−i6i6−22−2200000000000000000000000
χ6644-4-444-4-4-20000-2-222-2220000000002i3−2i32i3−2i300000000−22220000000000i6−i6i6−i62−22−200000000000000000000000
χ674-444-44-4-440000-44-44-4-4400000000000000000000000000000000000000000004i−4i0000000000000000000
χ684-444-44-4-440000-44-44-4-440000000000000000000000000000000000000000000−4i4i0000000000000000000
χ694-44-44-44-444-4-44-4-4444-4-40000004-440000-400000000000000000000000000000000000000000000000000
χ704-44-44-44-4-24-4-4422-2-2-222000000-22-2−2i3−2i32i32i320000000002i3−2i3000000000000000000000000000000000000000
χ714-44-44-44-4-24-4-4422-2-2-222000000-22-22i32i3−2i3−2i32000000000−2i32i3000000000000000000000000000000000000000
χ724-4-444-4-4440000-4-4-4-44444-400000004-4-44000000000000000000000000000000000000000000000000000
χ734-4-444-4-4440000-4-4-4-4444-440000000-444-4000000000000000000000000000000000000000000000000000
χ744-4-444-4-44-200002222-2-2-24-40000000-222-200000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ754-4-444-4-44-200002222-2-2-24-40000000-222-200000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ764-4-444-4-44-200002222-2-2-2-4400000002-2-2200000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ774-4-444-4-44-200002222-2-2-2-4400000002-2-2200000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ784-4-4-4-44444-44-44-444-4-44-4000000-4-440000400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-24-44-42-2-222-22004-4-44-2-220000200000000000-222-200000000000000000000000000000000000
χ804-4-4-4-4444-24-44-42-2-222-2200-444-4-2-2200002000000000002-2-2200000000000000000000000000000000000
χ814-4-4-4-4444-2-44-442-2-222-2200000022-20000-200000000000000023−23−23230000000000000000000000000000000
χ824-4-4-4-4444-2-44-442-2-222-2200000022-20000-2000000000000000−232323−230000000000000000000000000000000
χ83888-8-8-8-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000

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