Finite Group Databasebeta

← Group #10868271

Character table — Group #10868271

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
χ311111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
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
χ911111111111111111111-1-1111111-1-1-1-111-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-1-1-1-1111111-1-1-1
χ1011111111111111111111-1-1111111-1-1-1-111-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-11-1-111-1-1-111-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111111-1-11111-1-1-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-111-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-11-1-111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-111-111-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111-1-11111-1-111-1
χ17222222222-2-2-2-22222222220000-2-22222-2-2-200000000-2-2000000000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-200000000-2-20000000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000000022000000000000000022-2-22200000-200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-222-2-200000200000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-222-2-222-2-2111111-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-2-2-222111111-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-22222-2-22211-1-1-1-111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2-2-22222-2-211-1-1-1-11111-1-1-1-11111000000211-1-1000000000000
χ2922-2-2-2-22222-2-222-22-22-2-2000000220000-2-20002-200000022-2-20000000000002i−2i2i−2i000000002i−2i000000000
χ3022-2-2-2-22222-2-222-22-22-2-2000000220000-2-20002-200000022-2-2000000000000−2i2i−2i2i00000000−2i2i000000000
χ3122-2-2-2-22222-2-222-22-22-2-2000000220000-2-2000-22000000-2-2220000000000002i−2i2i−2i00000000−2i2i000000000
χ3222-2-2-2-22222-2-222-22-22-2-2000000220000-2-2000-22000000-2-222000000000000−2i2i−2i2i000000002i−2i000000000
χ3322-2-2-2-2222-222-22-22-22-2-2002i2i−2i−2i-2-20000220000000000000002i2i−2i−2i000000002i−2i−2i2i00000000002-20000000
χ3422-2-2-2-2222-222-22-22-22-2-2002i2i−2i−2i-2-20000220000000000000002i2i−2i−2i00000000−2i2i2i−2i0000000000-220000000
χ3522-2-2-2-2222-222-22-22-22-2-200−2i−2i2i2i-2-2000022000000000000000−2i−2i2i2i000000002i−2i−2i2i0000000000-220000000
χ3622-2-2-2-2222-222-22-22-22-2-200−2i−2i2i2i-2-2000022000000000000000−2i−2i2i2i00000000−2i2i2i−2i00000000002-20000000
χ372-222-2-22-22-22-22-2-222-22-2002i−2i2i−2i2-200002-20000000000000002i−2i2i−2i0000000000000000000000002i−2i2-2000
χ382-222-2-22-22-22-22-2-222-22-2002i−2i2i−2i2-200002-20000000000000002i−2i2i−2i000000000000000000000000−2i2i-22000
χ392-222-2-22-22-22-22-2-222-22-200−2i2i−2i2i2-200002-2000000000000000−2i2i−2i2i0000000000000000000000002i−2i-22000
χ402-222-2-22-22-22-22-2-222-22-200−2i2i−2i2i2-200002-2000000000000000−2i2i−2i2i000000000000000000000000−2i2i2-2000
χ412-2-2-2222-2222-2-2-222-2-2-22002-2-22-2200002-202i−2i002i−2i000000002-2-222i2i−2i−2i000000000002i−2i00000000000000
χ422-2-2-2222-2222-2-2-222-2-2-22002-2-22-2200002-20−2i2i00−2i2i000000002-2-22−2i−2i2i2i00000000000−2i2i00000000000000
χ432-2-2-2222-2222-2-2-222-2-2-2200-222-2-2200002-202i−2i00−2i2i00000000-222-2−2i−2i2i2i000000000002i−2i00000000000000
χ442-2-2-2222-2222-2-2-222-2-2-2200-222-2-2200002-20−2i2i002i−2i00000000-222-22i2i−2i−2i00000000000−2i2i00000000000000
χ452-2-2-2222-2-122-2-21-1-1111-1002-2-221-133−3−3-1102i−2i002i−2i003−33−33−3-111-1−i−iii−i3−i3i3i30000000−ii−i3i3000000000000
χ462-2-2-2222-2-122-2-21-1-1111-1002-2-221-133−3−3-110−2i2i00−2i2i003−33−33−3-111-1ii−i−ii3i3−i3−i30000000i−ii3−i3000000000000
χ472-2-2-2222-2-122-2-21-1-1111-1002-2-221-1−3−333-1102i−2i002i−2i00−33−33−33-111-1−i−iiii3i3−i3−i30000000−iii3−i3000000000000
χ482-2-2-2222-2-122-2-21-1-1111-1002-2-221-1−3−333-110−2i2i00−2i2i00−33−33−33-111-1ii−i−i−i3−i3i3i30000000i−i−i3i3000000000000
χ492-2-2-2222-2-122-2-21-1-1111-100-222-21-133−3−3-1102i−2i00−2i2i003−3−33−331-1-11ii−i−ii3i3−i3−i30000000−ii−i3i3000000000000
χ502-2-2-2222-2-122-2-21-1-1111-100-222-21-133−3−3-110−2i2i002i−2i003−3−33−331-1-11−i−iii−i3−i3i3i30000000i−ii3−i3000000000000
χ512-2-2-2222-2-122-2-21-1-1111-100-222-21-1−3−333-1102i−2i00−2i2i00−333−33−31-1-11ii−i−i−i3−i3i3i30000000−iii3−i3000000000000
χ522-2-2-2222-2-122-2-21-1-1111-100-222-21-1−3−333-110−2i2i002i−2i00−333−33−31-1-11−i−iiii3i3−i3−i30000000i−i−i3i3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-222-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-44-4-4-4400004-4-44-4-4400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ56444-44-4-4-4400004-4-44-4-44000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ57444-44-4-4-4-20000-222-222-20000000023−2323−2300000000022−2200000000006−66−6−22−2200000000000000000000000
χ58444-44-4-4-4-20000-222-222-20000000023−2323−23000000000−22220000000000−66−662−22−200000000000000000000000
χ59444-44-4-4-4-20000-222-222-200000000−2323−232300000000022−220000000000−66−66−22−2200000000000000000000000
χ60444-44-4-4-4-20000-222-222-200000000−2323−2323000000000−222200000000006−66−62−22−200000000000000000000000
χ6144-44-44-4-44000044-4-4-44-4000000000000000000000000000000000000000000000000000000000000022−220
χ6244-44-44-4-44000044-4-4-44-40000000000000000000000000000000000000000000000000000000000000−22220
χ6344-4-4-4-444-24-4-44-22-22-222000000-2-20000220004-4000000-2-22200000000000000000000000000000000000
χ6444-4-4-4-444-24-4-44-22-22-222000000-2-2000022000-4400000022-2-200000000000000000000000000000000000
χ6544-4-4-4-444-2-444-4-22-22-222004i4i−4i−4i220000-2-2000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6644-4-4-4-444-2-444-4-22-22-22200−4i−4i4i4i220000-2-20000000000000002i2i−2i−2i0000000000000000000000000000000
χ674-444-4-44-444-44-4-4-444-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ684-444-4-44-4-24-44-422-2-22-220000002-200002-20000000000023−23−232300000000000000000000000000000000000
χ694-444-4-44-4-24-44-422-2-22-220000002-200002-200000000000−232323−2300000000000000000000000000000000000
χ704-444-4-44-4-2-44-4422-2-22-22004i−4i4i−4i-220000-22000000000000000−2i2i−2i2i0000000000000000000000000000000
χ714-444-4-44-4-2-44-4422-2-22-2200−4i4i−4i4i-220000-220000000000000002i−2i2i−2i0000000000000000000000000000000
χ724-44-4-44-4440000-44-444-4-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ734-44-4-44-4440000-44-444-4-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ744-4-444-4-4440000-4-4-4-44444-40000004-4-440000000000000000000000000000000000000000000000000000
χ754-4-444-4-4440000-4-4-4-4444-44000000-444-40000000000000000000000000000000000000000000000000000
χ764-4-444-4-44-200002222-2-2-24-4000000-222-2000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ774-4-444-4-44-200002222-2-2-24-4000000-222-2000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ784-4-444-4-44-200002222-2-2-2-440000002-2-22000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ794-4-444-4-44-200002222-2-2-2-440000002-2-22000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ804-4-4-4444-44-4-444-444-4-4-440000004-40000-4400000000000000000000000000000000000000000000000000
χ814-4-4-4444-4-2-4-4442-2-2222-2000000-222323−23−232-2000000000−2323000000000000000000000000000000000000000
χ824-4-4-4444-4-2-4-4442-2-2222-2000000-22−23−2323232-200000000023−23000000000000000000000000000000000000000
χ8388-88-88-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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