Finite Group Databasebeta

← Group #10853383

Character table — Group #10853383

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212444422444448812121212242424242424242444444444888846612121212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-111-1-1111-1-111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111-1-111-111-1-111-1
χ911111111111111111111-1-111111111111111-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-111-1-1-1-111-1-1-111-1-1-1
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
χ1111111111111111111111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111111-1-1111
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
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111111111-1-11111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111-1-1-1-111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-111111-1-1-1-1-1-11
χ17222222222-2-2-2-22222222220000-2-2-2-22222000000-200-2-22200000000-2-20000220000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000-200-2-22200000000220000-2-2000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2222200000020022-2-200000000-2-20000-2-2000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200000020022-2-200000000220000220000000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002222-2-22-2-2-1-1-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-2-2-2222-2-2-1-1-1-111111111000000000000211-1-111-1-100000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2-2-22211111111-1-1-1-10000000000002-1-1-1-1111100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-22222-22211111111-1-1-1-1000000000000-21111-1-1-1-100000000
χ29222-2-2-22-2222-2-222-22-2-2-200000022-2-222-2-22-200000000000000000002-222-2-200000002-200000000000000
χ30222-2-2-22-2222-2-222-22-2-2-200000022-2-222-2-2-2200000000000000000002-2-2-2220000000-2200000000000000
χ31222-2-2-22-2222-2-222-22-2-2-200000022-2-2-2-2222-20000000000000000000-22-2-22200000002-200000000000000
χ32222-2-2-22-2222-2-222-22-2-2-200000022-2-2-2-222-220000000000000000000-2222-2-20000000-2200000000000000
χ33222-2-2-22-22-2-22222-22-2-2-2000000-2-22222-2-2002i−2i00000000000000000-220000000000000002i−2i0002i−2i00000
χ34222-2-2-22-22-2-22222-22-2-2-2000000-2-22222-2-200−2i2i00000000000000000-22000000000000000−2i2i000−2i2i00000
χ35222-2-2-22-22-2-22222-22-2-2-2000000-2-222-2-222002i−2i000000000000000002-20000000000000002i−2i000−2i2i00000
χ36222-2-2-22-22-2-22222-22-2-2-2000000-2-222-2-22200−2i2i000000000000000002-2000000000000000−2i2i0002i−2i00000
χ3722-222-2-2-222-2-22-2-222-2-220000002-2-22000000002-2000000000000000002i−2i2i−2i002i2i−2i−2i00000002-200000000
χ3822-222-2-2-222-2-22-2-222-2-220000002-2-22000000002-200000000000000000−2i2i−2i2i00−2i−2i2i2i00000002-200000000
χ3922-222-2-2-222-2-22-2-222-2-220000002-2-2200000000-22000000000000000002i−2i2i−2i00−2i−2i2i2i0000000-2200000000
χ4022-222-2-2-222-2-22-2-222-2-220000002-2-2200000000-2200000000000000000−2i2i−2i2i002i2i−2i−2i0000000-2200000000
χ4122-2-2-22-2222-22-2-2-2-2222-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i0000002i−2i−2i2i0000000000000000002-2000
χ4222-2-2-22-2222-22-2-2-2-2222-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i000000−2i2i2i−2i000000000000000000-22000
χ4322-2-2-22-2222-22-2-2-2-2222-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i0000002i−2i−2i2i000000000000000000-22000
χ4422-2-2-22-2222-22-2-2-2-2222-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i000000−2i2i2i−2i0000000000000000002-2000
χ452-222-22-2-2200002-2-2-2-2222-22−22−200002i−2i2i−2i00000002−2002-22−22−222−2−20000002i−2i−i2i2−i2i200000000000000−i2i20
χ462-222-22-2-2200002-2-2-2-2222-22−22−20000−2i2i−2i2i00000002−2002-22−22−222−2−2000000−2i2ii2−i2i2−i200000000000000i2−i20
χ472-222-22-2-2200002-2-2-2-2222-2−22−2200002i−2i2i−2i0000000−22002-2−22−22−2−2220000002i−2ii2−i2i2−i200000000000000i2−i20
χ482-222-22-2-2200002-2-2-2-2222-2−22−220000−2i2i−2i2i0000000−22002-2−22−22−2−222000000−2i2i−i2i2−i2i200000000000000−i2i20
χ492-222-22-2-2200002-2-2-2-222-222−22−200002i−2i2i−2i0000000−2200-222−22−2−2−222000000−2i2i−i2i2−i2i200000000000000i2−i20
χ502-222-22-2-2200002-2-2-2-222-222−22−20000−2i2i−2i2i0000000−2200-222−22−2−2−2220000002i−2ii2−i2i2−i200000000000000−i2i20
χ512-222-22-2-2200002-2-2-2-222-22−22−2200002i−2i2i−2i00000002−200-22−22−2222−2−2000000−2i2ii2−i2i2−i200000000000000−i2i20
χ522-222-22-2-2200002-2-2-2-222-22−22−220000−2i2i−2i2i00000002−200-22−22−2222−2−20000002i−2i−i2i2−i2i200000000000000i2−i20
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
χ55444-4-4-44-4-244-4-4-2-22-2222000000-2-22200004-400000000000000000000000000000000-2200000000000000
χ56444-4-4-44-4-244-4-4-2-22-2222000000-2-2220000-44000000000000000000000000000000002-200000000000000
χ57444-4-4-44-4-2-4-444-2-22-222200000022-2-20000004i−4i0000000000000000000000000000000000−2i2i0000000000
χ58444-4-4-44-4-2-4-444-2-22-222200000022-2-2000000−4i4i00000000000000000000000000000000002i−2i0000000000
χ5944-444-4-4-44-444-4-4-444-4-44000000-444-4000000000000000000000000000000000000000000000000000000
χ6044-444-4-4-4-24-4-4422-2-222-2000000-222-2000000004-40000000000000000000000000000000000-2200000000
χ6144-444-4-4-4-24-4-4422-2-222-2000000-222-200000000-4400000000000000000000000000000000002-200000000
χ6244-444-4-4-4-2-444-422-2-222-20000002-2-22000000000000000000000000000000000000000023−23000000000000
χ6344-444-4-4-4-2-444-422-2-222-20000002-2-220000000000000000000000000000000000000000−2323000000000000
χ6444-4-4-44-444-44-44-4-4-4444-4000000-44-44000000000000000000000000000000000000000000000000000000
χ6544-4-4-44-44-24-44-4222-2-2-22004i4i−4i−4i-22-2200000000000000000−2i−2i2i2i000000000000000000000000000000000
χ6644-4-4-44-44-24-44-4222-2-2-2200−4i−4i4i4i-22-22000000000000000002i2i−2i−2i000000000000000000000000000000000
χ6744-4-4-44-44-2-44-44222-2-2-220000002-22-2000000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ6844-4-4-44-44-2-44-44222-2-2-220000002-22-20000000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ694-444-44-4-4-20000-22222-2-24-422−2222−2200000000000000022−2200-22−22−22−2−22200000000000000000000000000000
χ704-444-44-4-4-20000-22222-2-24-4−2222−2222000000000000000−222200-222−22−222−2−200000000000000000000000000000
χ714-444-44-4-4-20000-22222-2-2-4422−2222−22000000000000000−2222002-2−22−2222−2−200000000000000000000000000000
χ724-444-44-4-4-20000-22222-2-2-44−2222−222200000000000000022−22002-22−22−2−2−22200000000000000000000000000000
χ734-44-44-4-44400004-44-44-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ744-44-44-4-44400004-44-44-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ754-4-44-4-44440000-44-4-44-44000000000000000000000000000000000000000000022−22−222200000000000000000
χ764-4-44-4-44440000-44-4-44-440000000000000000000000000000000000000000000−222222−2200000000000000000
χ774-4-4-4444-440000-444-4-44-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ784-4-4-4444-440000-444-4-44-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ794-4-4-4444-4-200002-2-222-2200−2i22i22i2−2i20000000000000000023−2300i2−i2−i2i2i6−i6−i6i600000000000000000000000000000
χ804-4-4-4444-4-200002-2-222-2200−2i22i22i2−2i200000000000000000−232300i2−i2−i2i2−i6i6i6−i600000000000000000000000000000
χ814-4-4-4444-4-200002-2-222-22002i2−2i2−2i22i20000000000000000023−2300−i2i2i2−i2−i6i6i6−i600000000000000000000000000000
χ824-4-4-4444-4-200002-2-222-22002i2−2i2−2i22i200000000000000000−232300−i2i2i2−i2i6−i6−i6i600000000000000000000000000000
χ838-88-88-8-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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