Finite Group Databasebeta

← Group #10868301

Character table — Group #10868301

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
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ71111111111111111111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-111-111-1-11111-1-1-1
χ1011111111111111111111-1-1111111-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1111-1-111-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-1-111-1-1-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-1-11-1-1111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-111-1-1-11111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-111111-1-1-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111111-1-1-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-111-1
χ17222222222-2-2-2-22222222220000-2-22222-2-200-200000000000000-2-20000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-22222222220000-2-22222-2-200-200000000000000-2-200000000-2-2222200000-200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-20020000000000000022000000002222-2-200000-200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000000000002200000000-2-2-2-22200000200000000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-211111111-1-1111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22-2-2222211111111-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-22222-2-2-1-1-1-1111111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-2-2-222-1-1-1-11111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-222-2-2221111-1-1-1-1111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-2-222-2-21111-1-1-1-111-1-1-1-111110000002-1-111000000000000
χ2922-22-22-2-22-22-22-222-2-2-22002i2i−2i−2i2-200002-20000000002i2i−2i−2i0000000000000000000000000000002i−2i2-2000
χ3022-22-22-2-22-22-22-222-2-2-22002i2i−2i−2i2-200002-20000000002i2i−2i−2i000000000000000000000000000000−2i2i-22000
χ3122-22-22-2-22-22-22-222-2-2-2200−2i−2i2i2i2-200002-2000000000−2i−2i2i2i0000000000000000000000000000002i−2i-22000
χ3222-22-22-2-22-22-22-222-2-2-2200−2i−2i2i2i2-200002-2000000000−2i−2i2i2i000000000000000000000000000000−2i2i2-2000
χ332-22-2-22-2222-2-2222-22-2-2-2000000220000-2-22-20000000000022-2-200000000002i−2i002i−2i000000002i−2i0000000
χ342-22-2-22-2222-2-2222-22-2-2-2000000220000-2-22-20000000000022-2-20000000000−2i2i00−2i2i00000000−2i2i0000000
χ352-22-2-22-2222-2-2222-22-2-2-2000000220000-2-2-2200000000000-2-22200000000002i−2i002i−2i00000000−2i2i0000000
χ362-22-2-22-2222-2-2222-22-2-2-2000000220000-2-2-2200000000000-2-2220000000000−2i2i00−2i2i000000002i−2i0000000
χ372-22-2-22-222-222-222-22-2-2-2002i−2i2i−2i-2-20000220000000002i−2i2i−2i000000000000002i−2i00−2i2i0000002-2000000000
χ382-22-2-22-222-222-222-22-2-2-2002i−2i2i−2i-2-20000220000000002i−2i2i−2i00000000000000−2i2i002i−2i000000-22000000000
χ392-22-2-22-222-222-222-22-2-2-200−2i2i−2i2i-2-2000022000000000−2i2i−2i2i000000000000002i−2i00−2i2i000000-22000000000
χ402-22-2-22-222-222-222-22-2-2-200−2i2i−2i2i-2-2000022000000000−2i2i−2i2i00000000000000−2i2i002i−2i0000002-2000000000
χ412-2-2-2222-2222-2-2-22-2-222-2002-2-22-2200002-20002i−2i2i−2i002-2-220000002i2i−2i−2i00000000000002i−2i000000000000
χ422-2-2-2222-2222-2-2-22-2-222-2002-2-22-2200002-2000−2i2i−2i2i002-2-22000000−2i−2i2i2i0000000000000−2i2i000000000000
χ432-2-2-2222-2222-2-2-22-2-222-200-222-2-2200002-20002i−2i−2i2i00-222-2000000−2i−2i2i2i00000000000002i−2i000000000000
χ442-2-2-2222-2222-2-2-22-2-222-200-222-2-2200002-2000−2i2i2i−2i00-222-20000002i2i−2i−2i0000000000000−2i2i000000000000
χ452-2-2-2222-2-122-2-21-111-1-11002-2-221-133−3−3-110002i−2i2i−2i00-111-13−33−33−3−i−iii−i3−i3i3i30000000−i3i3−ii000000000000
χ462-2-2-2222-2-122-2-21-111-1-11002-2-221-133−3−3-11000−2i2i−2i2i00-111-13−33−33−3ii−i−ii3i3−i3−i30000000i3−i3i−i000000000000
χ472-2-2-2222-2-122-2-21-111-1-11002-2-221-1−3−333-110002i−2i2i−2i00-111-1−33−33−33−i−iiii3i3−i3−i30000000i3−i3−ii000000000000
χ482-2-2-2222-2-122-2-21-111-1-11002-2-221-1−3−333-11000−2i2i−2i2i00-111-1−33−33−33ii−i−i−i3−i3i3i30000000−i3i3i−i000000000000
χ492-2-2-2222-2-122-2-21-111-1-1100-222-21-133−3−3-110002i−2i−2i2i001-1-11−33−333−3ii−i−ii3i3−i3−i30000000−i3i3−ii000000000000
χ502-2-2-2222-2-122-2-21-111-1-1100-222-21-133−3−3-11000−2i2i2i−2i001-1-11−33−333−3−i−iii−i3−i3i3i30000000i3−i3i−i000000000000
χ512-2-2-2222-2-122-2-21-111-1-1100-222-21-1−3−333-110002i−2i−2i2i001-1-113−33−3−33ii−i−i−i3−i3i3i30000000i3−i3−ii000000000000
χ522-2-2-2222-2-122-2-21-111-1-1100-222-21-1−3−333-11000−2i2i2i−2i001-1-113−33−3−33−i−iiii3i3−i3−i30000000−i3i3i−i000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-22200-400000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222222200400000000000000-2-20000000000000000000000000000000
χ55444-44-4-4-440000-4-4444-4-44-40000004-44-40000000000000000000000000000000000000000000000000000
χ56444-44-4-4-440000-4-4444-4-4-44000000-44-440000000000000000000000000000000000000000000000000000
χ57444-44-4-4-4-2000022-2-2-2224-4000000-22-220000000000000000000006−66−66−66−600000000000000000000000
χ58444-44-4-4-4-2000022-2-2-2224-4000000-22-22000000000000000000000−66−66−66−6600000000000000000000000
χ59444-44-4-4-4-2000022-2-2-222-440000002-22-20000000000000000000006−66−6−66−6600000000000000000000000
χ60444-44-4-4-4-2000022-2-2-222-440000002-22-2000000000000000000000−66−666−66−600000000000000000000000
χ6144-44-44-4-444-44-4-444-4-4-44000000-440000-4400000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-24-44-42-2-2222-20000002-200002-2000000000000023−23−2323000000000000000000000000000000000
χ6344-44-44-4-4-24-44-42-2-2222-20000002-200002-20000000000000−232323−23000000000000000000000000000000000
χ6444-44-44-4-4-2-44-442-2-2222-2004i4i−4i−4i-220000-22000000000−2i−2i2i2i0000000000000000000000000000000000000
χ6544-44-44-4-4-2-44-442-2-2222-200−4i−4i4i4i-220000-220000000002i2i−2i−2i0000000000000000000000000000000000000
χ6644-4-4-4-444400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ6744-4-4-4-444400004-44-4-44-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ684-444-4-44-440000-4-4-44-44400000000000000000000000000000000000000000004i−4i0000000000000000000
χ694-444-4-44-440000-4-4-44-4440000000000000000000000000000000000000000000−4i4i0000000000000000000
χ704-44-4-44-44-24-4-44-2-22-2222000000-2-20000224-400000000000-2-222000000000000000000000000000000000
χ714-44-4-44-44-24-4-44-2-22-2222000000-2-2000022-440000000000022-2-2000000000000000000000000000000000
χ724-44-4-44-44-2-444-4-2-22-2222004i−4i4i−4i220000-2-2000000000−2i2i−2i2i0000000000000000000000000000000000000
χ734-44-4-44-44-2-444-4-2-22-222200−4i4i−4i4i220000-2-20000000002i−2i2i−2i0000000000000000000000000000000000000
χ744-4-444-4-44400004-4-4-44-44000000000000000000000−2i22i200000000000000−2i22i22i2−2i200000000000000000000000
χ754-4-444-4-44400004-4-4-44-440000000000000000000002i2−2i2000000000000002i2−2i2−2i22i200000000000000000000000
χ764-4-444-4-44-20000-2222-22-20000000023−23−2323000000000−2i22i20000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ774-4-444-4-44-20000-2222-22-20000000023−23−23230000000002i2−2i20000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ784-4-444-4-44-20000-2222-22-200000000−232323−23000000000−2i22i20000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ794-4-444-4-44-20000-2222-22-200000000−232323−230000000002i2−2i20000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ804-4-4-4444-44-4-444-44-4-444-40000004-40000-4400000000000000000000000000000000000000000000000000
χ814-4-4-4444-4-2-4-4442-222-2-22000000-222323−23−232-200000000000000000−23230000000000000000000000000000000
χ824-4-4-4444-4-2-4-4442-222-2-22000000-22−23−2323232-20000000000000000023−230000000000000000000000000000000
χ8388-8-8-8-888-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-88-8-40000444-44-4-40000000000000000000000000000000000000000000000000000000000000000

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