Finite Group Databasebeta

← Group #10853245

Character table — Group #10853245

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
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ71111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-111-11111-1-1-1
χ1011111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-111-1-11-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11-1-111-1-111-1-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11111-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-1-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-11-1-11111-1-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-111-1-111111-1-111-1
χ17222222222-2-2-2-22222222220000-2-22222-2-200-2000000-2-2000000000000000022-2-222000000000-20000000
χ18222222222-2-2-2-22222222220000-2-22222-2-200-2000000-2-20000000000000000-2-222-2-200000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200200000022000000000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000220000000000000000-2-22222000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-122-2-2-2-2-22211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-22222-2-2111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2-2-222-2-222111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ2922-22-2-22-2222-2-222-22-2-2-20022-2-2220000-2-20000000000022-2-20000000000002-22-20000000002-200000000
χ3022-22-2-22-2222-2-222-22-2-2-20022-2-2220000-2-20000000000022-2-2000000000000-22-22000000000-2200000000
χ3122-22-2-22-2222-2-222-22-2-2-200-2-222220000-2-200000000000-2-2220000000000002-22-2000000000-2200000000
χ3222-22-2-22-2222-2-222-22-2-2-200-2-222220000-2-200000000000-2-222000000000000-22-220000000002-200000000
χ3322-22-2-22-22-2-22222-22-2-2-2000000-2-20000220002i−2i00000000002i2i−2i−2i000000002-2-2200000002i−2i0000000000
χ3422-22-2-22-22-2-22222-22-2-2-2000000-2-20000220002i−2i00000000002i2i−2i−2i00000000-222-20000000−2i2i0000000000
χ3522-22-2-22-22-2-22222-22-2-2-2000000-2-2000022000−2i2i0000000000−2i−2i2i2i000000002-2-220000000−2i2i0000000000
χ3622-22-2-22-22-2-22222-22-2-2-2000000-2-2000022000−2i2i0000000000−2i−2i2i2i00000000-222-200000002i−2i0000000000
χ372-222-22-2-222-2-22-222-2-2-22002i−2i2i−2i2-200002-2000000000002i−2i2i−2i00000000000000000000000000002i−2i2-2000
χ382-222-22-2-222-2-22-222-2-2-22002i−2i2i−2i2-200002-2000000000002i−2i2i−2i0000000000000000000000000000−2i2i-22000
χ392-222-22-2-222-2-22-222-2-2-2200−2i2i−2i2i2-200002-200000000000−2i2i−2i2i00000000000000000000000000002i−2i-22000
χ402-222-22-2-222-2-22-222-2-2-2200−2i2i−2i2i2-200002-200000000000−2i2i−2i2i0000000000000000000000000000−2i2i2-2000
χ412-2-222-2-2222-22-2-22-2-222-2002i−2i−2i2i2-20000-222-2000002i−2i002i−2i−2i2i00002i2i−2i−2i000000000002-200000000000000
χ422-2-222-2-2222-22-2-22-2-222-2002i−2i−2i2i2-20000-22-2200000−2i2i002i−2i−2i2i0000−2i−2i2i2i00000000000-2200000000000000
χ432-2-222-2-2222-22-2-22-2-222-200−2i2i2i−2i2-20000-222-200000−2i2i00−2i2i2i−2i0000−2i−2i2i2i000000000002-200000000000000
χ442-2-222-2-2222-22-2-22-2-222-200−2i2i2i−2i2-20000-22-22000002i−2i00−2i2i2i−2i00002i2i−2i−2i00000000000-2200000000000000
χ452-2-222-2-22-12-22-21-111-1-11002i−2i−2i2i-1133−3−31-12-2000002i−2i3−3−iii−i−i3i3−i3i3−i−iii−i3−i3i3i30000000-113−3000000000000
χ462-2-222-2-22-12-22-21-111-1-11002i−2i−2i2i-1133−3−31-1-2200000−2i2i3−3−iii−i−i3i3−i3i3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ472-2-222-2-22-12-22-21-111-1-11002i−2i−2i2i-11−3−3331-12-2000002i−2i−33−iii−ii3−i3i3−i3−i−iiii3i3−i3−i30000000-11−33000000000000
χ482-2-222-2-22-12-22-21-111-1-11002i−2i−2i2i-11−3−3331-1-2200000−2i2i−33−iii−ii3−i3i3−i3ii−i−i−i3−i3i3i300000001-13−3000000000000
χ492-2-222-2-22-12-22-21-111-1-1100−2i2i2i−2i-1133−3−31-12-200000−2i2i3−3i−i−iii3−i3i3−i3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ502-2-222-2-22-12-22-21-111-1-1100−2i2i2i−2i-1133−3−31-1-22000002i−2i3−3i−i−iii3−i3i3−i3−i−iii−i3−i3i3i300000001-1−33000000000000
χ512-2-222-2-22-12-22-21-111-1-1100−2i2i2i−2i-11−3−3331-12-200000−2i2i−33i−i−ii−i3i3−i3i3ii−i−i−i3−i3i3i30000000-11−33000000000000
χ522-2-222-2-22-12-22-21-111-1-1100−2i2i2i−2i-11−3−3331-1-22000002i−2i−33i−i−ii−i3i3−i3i3−i−iiii3i3−i3−i300000001-13−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-22200-400000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222004000000-2-2000000000000000000000000000000000000000
χ55444-44-4-4-4400004-4-4-44-444-40000004-44-40000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4400004-4-4-44-44-44000000-44-440000000000000000000000000000000000000000000000000000
χ57444-44-4-4-4-20000-2222-22-24-4000000-22-220000000000000000000006−66−66−66−600000000000000000000000
χ58444-44-4-4-4-20000-2222-22-24-4000000-22-22000000000000000000000−66−66−66−6600000000000000000000000
χ59444-44-4-4-4-20000-2222-22-2-440000002-22-20000000000000000000006−66−6−66−6600000000000000000000000
χ60444-44-4-4-4-20000-2222-22-2-440000002-22-2000000000000000000000−66−666−66−600000000000000000000000
χ6144-44-4-44-4-244-4-4-2-22-22220044-4-4-2-200002200000000000-2-22200000000000000000000000000000000000
χ6244-44-4-44-4-244-4-4-2-22-222200-4-444-2-20000220000000000022-2-200000000000000000000000000000000000
χ6344-44-4-44-4-2-4-444-2-22-2222000000220000-2-20004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000
χ6444-44-4-44-4-2-4-444-2-22-2222000000220000-2-2000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000
χ6544-4-4-44-44400004-44-4-44-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ6644-4-4-44-44400004-44-4-44-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ674-444-44-4-44-444-4-444-4-4-44000000-440000-4400000000000000000000000000000000000000000000000000
χ684-444-44-4-4-24-4-442-2-2222-2004i−4i4i−4i-220000-2200000000000−2i2i−2i2i00000000000000000000000000000000000
χ694-444-44-4-4-24-4-442-2-2222-200−4i4i−4i4i-220000-22000000000002i−2i2i−2i00000000000000000000000000000000000
χ704-444-44-4-4-2-444-42-2-2222-20000002-200002-200000000000000023−23−23230000000000000000000000000000000
χ714-444-44-4-4-2-444-42-2-2222-20000002-200002-2000000000000000−232323−230000000000000000000000000000000
χ724-44-4-4-44440000-4-4-44-444000000000000000000000000000000000000000000000000000000000000022−220
χ734-44-4-4-44440000-4-4-44-4440000000000000000000000000000000000000000000000000000000000000−22220
χ744-4-444-4-444-44-44-44-4-444-4000000-4400004-400000000000000000000000000000000000000000000000000
χ754-4-444-4-44-2-44-442-222-2-220000002-22323−23−23-22000000000−2323000000000000000000000000000000000000000
χ764-4-444-4-44-2-44-442-222-2-220000002-2−23−232323-2200000000023−23000000000000000000000000000000000000000
χ774-4-4-4444-440000-4-4444-4-40000000000000000000−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000
χ784-4-4-4444-440000-4-4444-4-400000000000000000002i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000
χ794-4-4-4444-4-2000022-2-2-2220000000023−23−23230000000−2i22i2000000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ804-4-4-4444-4-2000022-2-2-2220000000023−23−232300000002i2−2i2000000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ814-4-4-4444-4-2000022-2-2-22200000000−232323−230000000−2i22i2000000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ824-4-4-4444-4-2000022-2-2-22200000000−232323−2300000002i2−2i2000000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ8388-8-8-88-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-8-888-40000444-44-4-40000000000000000000000000000000000000000000000000000000000000000

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