Finite Group Databasebeta

← Group #10875943

Character table — Group #10875943

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424444444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ5111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-111-1-11111-1-1-111-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1111-1-1111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-111-1-111-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-11111-1-111111-1-1-1
χ911111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1111111-1
χ1111111111111111111111-1-1-1-11111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-111-1-111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1111-1-111-1-1-1-1-11111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11-1-11111111-1-1-1-111-1
χ17222222222-2-2-2-222222220000222222-2-2-2-200-2000000-2-200000000000000002222-2-2000000000-20000000
χ18222222222-2-2-2-222222220000222222-2-2-2-200-2000000-2-20000000000000000-2-2-2-22200000000020000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200200000022000000000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2002000000220000000000000000-2-22222000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-122-2-2-2-2-222111111-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-222-2-2111111-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-22222-2-211-1-1-1-111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-2-222-2-22211-1-1-1-11111-1-1-1-11111000000211-1-1000000000000
χ2922-222-2-2-22-22-222-2-2-22-2222-2-2000000-2-22200000000000000022-2-200000000000000000002i−2i000002i−2i000
χ3022-222-2-2-22-22-222-2-2-22-2222-2-2000000-2-22200000000000000022-2-20000000000000000000−2i2i00000−2i2i000
χ3122-222-2-2-22-22-222-2-2-22-22-2-222000000-2-222000000000000000-2-22200000000000000000002i−2i00000−2i2i000
χ3222-222-2-2-22-22-222-2-2-22-22-2-222000000-2-222000000000000000-2-2220000000000000000000−2i2i000002i−2i000
χ332-222-2-22-222-2-22-2-2-22-22200000000002-22-20002-200000022-2-20000000000002i−2i002i−2i00000000002i−2i00000
χ342-222-2-22-222-2-22-2-2-22-22200000000002-22-20002-200000022-2-2000000000000−2i2i00−2i2i0000000000−2i2i00000
χ352-222-2-22-222-2-22-2-2-22-22200000000002-22-2000-22000000-2-2220000000000002i−2i002i−2i0000000000−2i2i00000
χ362-222-2-22-222-2-22-2-2-22-22200000000002-22-2000-22000000-2-222000000000000−2i2i00−2i2i00000000002i−2i00000
χ372-222-2-22-22-222-2-2-2-22-2222-22-2000000-22-220000000000000002-22-2000000002i−2i00−2i2i00000002i−2i00000000
χ382-222-2-22-22-222-2-2-2-22-2222-22-2000000-22-220000000000000002-22-200000000−2i2i002i−2i0000000−2i2i00000000
χ392-222-2-22-22-222-2-2-2-22-222-22-22000000-22-22000000000000000-22-22000000002i−2i00−2i2i0000000−2i2i00000000
χ402-222-2-22-22-222-2-2-2-22-222-22-22000000-22-22000000000000000-22-2200000000−2i2i002i−2i00000002i−2i00000000
χ412-2-22-22-22222-2-2-222-2-2-222-2-220000002-2-222i−2i000002i−2i0000002-2-222i2i−2i−2i000000000002i−2i00000000000000
χ422-2-22-22-22222-2-2-222-2-2-222-2-220000002-2-22−2i2i00000−2i2i0000002-2-22−2i−2i2i2i00000000000−2i2i00000000000000
χ432-2-22-22-22222-2-2-222-2-2-22-222-20000002-2-222i−2i00000−2i2i000000-222-2−2i−2i2i2i000000000002i−2i00000000000000
χ442-2-22-22-22222-2-2-222-2-2-22-222-20000002-2-22−2i2i000002i−2i000000-222-22i2i−2i−2i00000000000−2i2i00000000000000
χ452-2-22-22-22-122-2-21-1-1111-12-2-220033−3−3-111-12i−2i000002i−2i3−33−33−3-111-1−i−iii−i3−i3i3i30000000−ii−i3i3000000000000
χ462-2-22-22-22-122-2-21-1-1111-12-2-220033−3−3-111-1−2i2i00000−2i2i3−33−33−3-111-1ii−i−ii3i3−i3−i30000000i−ii3−i3000000000000
χ472-2-22-22-22-122-2-21-1-1111-12-2-2200−3−333-111-12i−2i000002i−2i−33−33−33-111-1−i−iiii3i3−i3−i30000000−iii3−i3000000000000
χ482-2-22-22-22-122-2-21-1-1111-12-2-2200−3−333-111-1−2i2i00000−2i2i−33−33−33-111-1ii−i−i−i3−i3i3i30000000i−i−i3i3000000000000
χ492-2-22-22-22-122-2-21-1-1111-1-222-20033−3−3-111-12i−2i00000−2i2i3−3−33−331-1-11ii−i−ii3i3−i3−i30000000−ii−i3i3000000000000
χ502-2-22-22-22-122-2-21-1-1111-1-222-20033−3−3-111-1−2i2i000002i−2i3−3−33−331-1-11−i−iii−i3−i3i3i30000000i−ii3−i3000000000000
χ512-2-22-22-22-122-2-21-1-1111-1-222-200−3−333-111-12i−2i00000−2i2i−333−33−31-1-11ii−i−i−i3−i3i3i30000000−iii3−i3000000000000
χ522-2-22-22-22-122-2-21-1-1111-1-222-200−3−333-111-1−2i2i000002i−2i−333−33−31-1-11−i−iiii3i3−i3−i30000000i−i−i3i3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-2222200-400000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-422222222004000000-2-2000000000000000000000000000000000000000
χ55444-4-44-4-440000-44-4-444-4000000000000000000022−22000000000000000022−2222−2200000000000000000000000
χ56444-4-44-4-440000-44-4-444-40000000000000000000−22220000000000000000−2222−222200000000000000000000000
χ57444-4-44-4-4-200002-222-2-2200000023−2323−2300000000022−220000000000006−66−6−22−2200000000000000000000000
χ58444-4-44-4-4-200002-222-2-2200000023−2323−23000000000−2222000000000000−66−662−22−200000000000000000000000
χ59444-4-44-4-4-200002-222-2-22000000−2323−232300000000022−22000000000000−66−66−22−2200000000000000000000000
χ60444-4-44-4-4-200002-222-2-22000000−2323−2323000000000−22220000000000006−66−62−22−200000000000000000000000
χ6144-444-4-4-444-44-44-4-4-44-44000000000044-4-400000000000000000000000000000000000000000000000000
χ6244-444-4-4-4-24-44-4-2222-22-20000000000-2-2220000000000023−23−232300000000000000000000000000000000000
χ6344-444-4-4-4-24-44-4-2222-22-20000000000-2-22200000000000−232323−2300000000000000000000000000000000000
χ6444-444-4-4-4-2-44-44-2222-22-244-4-400000022-2-2000000000000000-2-2220000000000000000000000000000000
χ6544-444-4-4-4-2-44-44-2222-22-2-4-44400000022-2-200000000000000022-2-20000000000000000000000000000000
χ6644-4-4-4-44440000-4-4444-4-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ6744-4-4-4-44440000-4-4444-4-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ684-444-4-44-4-24-4-44222-22-2-20000000000-22-220004-4000000-2-22200000000000000000000000000000000000
χ694-444-4-44-4-24-4-44222-22-2-20000000000-22-22000-4400000022-2-200000000000000000000000000000000000
χ704-444-4-44-4-2-444-4222-22-2-24-44-40000002-22-2000000000000000-22-220000000000000000000000000000000
χ714-444-4-44-4-2-444-4222-22-2-2-44-440000002-22-20000000000000002-22-20000000000000000000000000000000
χ724-44-44-4-44400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ734-44-44-4-44400004-44-4-44-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ744-4-44-44-444-4-444-444-4-4-440000000000-444-400000000000000000000000000000000000000000000000000
χ754-4-44-44-44-2-4-4442-2-2222-20000002323−23−232-2-22000000000−2323000000000000000000000000000000000000000
χ764-4-44-44-44-2-4-4442-2-2222-2000000−23−2323232-2-2200000000023−23000000000000000000000000000000000000000
χ774-4-4-4444-44000044-44-4-4-400004-44-4-44000000000000000000000000000000000000000000000000000000
χ784-4-4-4444-44000044-44-4-4-40000-44-444-4000000000000000000000000000000000000000000000000000000
χ794-4-4-4444-4-20000-2-22-222200004-4-222-200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ804-4-4-4444-4-20000-2-22-222200004-4-222-200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ814-4-4-4444-4-20000-2-22-22220000-442-2-2200000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ824-4-4-4444-4-20000-2-22-22220000-442-2-2200000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ8388-8-8-8-888-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000

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