Finite Group Databasebeta

← Group #10863706

Character table — Group #10863706

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order12222222344446666666448888121212124444222244488121212122424242424242424444444448888466661212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-111-1-111-1
χ911111111111111111111-1-111111111111111-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-111-1-1-1-111-1-1-111-1-1-1
χ1011111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-11111-1-1-111-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1111
χ1211111111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-11111-1-11-1-11111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111111111-1-11111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1111111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111111-1-111-1-111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-22222222220000-2-2-2-22222000000-200-2-22200000000-2-22200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000-200-2-2220000000022-2-20000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2222200000020022-2-200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200000020022-2-200000000222200000000000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-2-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002222-2-22-2-2-1-1-1-111111111000000000000-2-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-2-2-2222-2-2-1-1-1-11111111100000000000021111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-222-2-2-21111-1-1-1-11111000000000000-2-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-222-2-2-2-2-21111-1-1-1-11111000000000000211-1-1-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2-2-22211111111-1-1-1-10000000000002-1-111-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-22222-22211111111-1-1-1-1000000000000-211-1-111-1-100000000
χ29222-2-2-22-22-2-22222-22-2-2-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i000000002i2i−2i−2i00000000000000002-2000
χ30222-2-2-22-22-2-22222-22-2-2-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i00000000−2i−2i2i2i0000000000000000-22000
χ31222-2-2-22-22-2-22222-22-2-2-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i000000002i2i−2i−2i0000000000000000-22000
χ32222-2-2-22-22-2-22222-22-2-2-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i00000000−2i−2i2i2i00000000000000002-2000
χ3322-22-22-2-2200002-2-2-2-2222-22−22−200002i2i−2i−2i00000002−2002-22−22−222−2−2002i−2i0000−i2−i2i2i200000000000000−i2i20
χ3422-22-22-2-2200002-2-2-2-2222-22−22−20000−2i−2i2i2i00000002−2002-22−22−222−2−200−2i2i0000i2i2−i2−i200000000000000i2−i20
χ3522-22-22-2-2200002-2-2-2-2222-2−22−2200002i2i−2i−2i0000000−22002-2−22−22−2−222002i−2i0000i2i2−i2−i200000000000000i2−i20
χ3622-22-22-2-2200002-2-2-2-2222-2−22−220000−2i−2i2i2i0000000−22002-2−22−22−2−22200−2i2i0000−i2−i2i2i200000000000000−i2i20
χ3722-22-22-2-2200002-2-2-2-222-222−22−200002i2i−2i−2i0000000−2200-222−22−2−2−22200−2i2i0000−i2−i2i2i200000000000000i2−i20
χ3822-22-22-2-2200002-2-2-2-222-222−22−20000−2i−2i2i2i0000000−2200-222−22−2−2−222002i−2i0000i2i2−i2−i200000000000000−i2i20
χ3922-22-22-2-2200002-2-2-2-222-22−22−2200002i2i−2i−2i00000002−200-22−22−2222−2−200−2i2i0000i2i2−i2−i200000000000000−i2i20
χ4022-22-22-2-2200002-2-2-2-222-22−22−220000−2i−2i2i2i00000002−200-22−22−2222−2−2002i−2i0000−i2−i2i2i200000000000000i2−i20
χ412-2222-2-2-222-2-22-2-2-222-22000000-222-22i−2i2i−2i002-2000000000000000002i−2i00000000000002-2000002i−2i00000
χ422-2222-2-2-222-2-22-2-2-222-22000000-222-22i−2i2i−2i00-22000000000000000002i−2i0000000000000-2200000−2i2i00000
χ432-2222-2-2-222-2-22-2-2-222-22000000-222-2−2i2i−2i2i002-200000000000000000−2i2i00000000000002-200000−2i2i00000
χ442-2222-2-2-222-2-22-2-2-222-22000000-222-2−2i2i−2i2i00-2200000000000000000−2i2i0000000000000-22000002i−2i00000
χ452-2222-2-2-22-222-2-2-2-222-220000002-2-222i−2i2i−2i2-20000000000000000000−2i2i002i−2i2i−2i000002-200000000000000
χ462-2222-2-2-22-222-2-2-2-222-220000002-2-222i−2i2i−2i-220000000000000000000−2i2i00−2i2i−2i2i00000-2200000000000000
χ472-2222-2-2-22-222-2-2-2-222-220000002-2-22−2i2i−2i2i2-200000000000000000002i−2i00−2i2i−2i2i000002-200000000000000
χ482-2222-2-2-22-222-2-2-2-222-220000002-2-22−2i2i−2i2i-2200000000000000000002i−2i002i−2i2i−2i00000-2200000000000000
χ492-22-2-22-2222-22-2-2-222-22-200000022-2-2000000002i−2i00000000000000000002-2-222i−2i2i−2i00000002i−2i00000000
χ502-22-2-22-2222-22-2-2-222-22-200000022-2-2000000002i−2i0000000000000000000-222-2−2i2i−2i2i00000002i−2i00000000
χ512-22-2-22-2222-22-2-2-222-22-200000022-2-200000000−2i2i00000000000000000002-2-22−2i2i−2i2i0000000−2i2i00000000
χ522-22-2-22-2222-22-2-2-222-22-200000022-2-200000000−2i2i0000000000000000000-222-22i−2i2i−2i0000000−2i2i00000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000000000-40022-2-20000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022220000000000400-2-2220000000000000000000000000000000000000
χ55444-4-4-44-4444-4-444-44-4-4-4000000-44-44000000000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-244-4-4-2-22-22220000002-22-200000000000000000000023−2323−2300000000000000000000000000000
χ57444-4-4-44-4-244-4-4-2-22-22220000002-22-2000000000000000000000−2323−232300000000000000000000000000000
χ58444-4-4-44-4-2-4-444-2-22-2222004i4i−4i−4i-22-2200000000000000000−2i−2i2i2i000000000000000000000000000000000
χ59444-4-4-44-4-2-4-444-2-22-222200−4i−4i4i4i-22-22000000000000000002i2i−2i−2i000000000000000000000000000000000
χ6044-44-44-4-4-20000-22222-2-24-422−2222−2200000000000000022−2200-22−22−22−2−22200000000000000000000000000000
χ6144-44-44-4-4-20000-22222-2-24-4−2222−2222000000000000000−222200-222−22−222−2−200000000000000000000000000000
χ6244-44-44-4-4-20000-22222-2-2-4422−2222−22000000000000000−2222002-2−22−2222−2−200000000000000000000000000000
χ6344-44-44-4-4-20000-22222-2-2-44−2222−222200000000000000022−22002-22−22−2−2−22200000000000000000000000000000
χ6444-4-44-4-44400004-44-44-4-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ6544-4-44-4-44400004-44-44-4-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ6644-4-44-4-44-20000-22-22-22200−2i22i22i2−2i200000000000000000−2i32i300i2−i2−i2i26−6−6600000000000000000000000000000
χ6744-4-44-4-44-20000-22-22-22200−2i22i22i2−2i2000000000000000002i3−2i300i2−i2−i2i2−666−600000000000000000000000000000
χ6844-4-44-4-44-20000-22-22-222002i2−2i2−2i22i200000000000000000−2i32i300−i2i2i2−i2−666−600000000000000000000000000000
χ6944-4-44-4-44-20000-22-22-222002i2−2i2−2i22i2000000000000000002i3−2i300−i2i2i2−i26−6−6600000000000000000000000000000
χ704-4444-4-4-4-24-4-44222-2-22-20000002-2-220000004-400000000000000000000000000000000-22000000000000
χ714-4444-4-4-4-24-4-44222-2-22-20000002-2-22000000-44000000000000000000000000000000002-2000000000000
χ724-4444-4-4-4-2-444-4222-2-22-2000000-222-200004-400000000000000000000000000000000-2200000000000000
χ734-4444-4-4-4-2-444-4222-2-22-2000000-222-20000-44000000000000000000000000000000002-200000000000000
χ744-44-4-44-444-44-44-4-444-44-4000000-4-444000000000000000000000000000000000000000000000000000000
χ754-44-4-44-44-24-44-422-2-22-22000000-2-222000000004i−4i0000000000000000000000000000000000−2i2i00000000
χ764-44-4-44-44-24-44-422-2-22-22000000-2-22200000000−4i4i00000000000000000000000000000000002i−2i00000000
χ774-44-4-44-44-2-44-4422-2-22-2200000022-2-2000000000000000000000000000000000000000000−2i32i30000000000
χ784-44-4-44-44-2-44-4422-2-22-2200000022-2-20000000000000000000000000000000000000000002i3−2i30000000000
χ794-4-44-4-44440000-444-4-4-4400000000004-4-4400000000000000000000000000000000000000000000000000
χ804-4-44-4-44440000-444-4-4-440000000000-444-400000000000000000000000000000000000000000000000000
χ814-4-4-4444-440000-44-4-444-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ824-4-4-4444-440000-44-4-444-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ838-8-88-8-888-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

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