Finite Group Databasebeta

← Group #10827376

Character table — Group #10827376

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212222222444448812121212242424242424242444444444888846612121212121222222884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-111-1-1111
χ911111111111111111111-1-111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111111111-111-1-111-1-1-111-1-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-111-1-111-1-1-111-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11-1-111111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111111-1-111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1111111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-111-1-111-1-1-1-1-1-1-1-11111-1-11111111111-111-1-1-1-1111-1-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2222200-200000022-2-200000000-2-22200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-200-200000022-2-20000000022-2-20000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222002000000-2-22200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000-2-22200000000222200000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000222-2-2-2-2-2-2-1-1-1-1111111110000000000002-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-222222-2-2-1-1-1-111111111000000000000-21111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-2-222-2-21111-1-1-1-11111000000000000-2-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-222-2-2-2-21111-1-1-1-11111000000000000211-1-111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-222-2-22211111111-1-1-1-1000000000000-2-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-2-2-2222211111111-1-1-1-1000000000000211-1-1-1-11100000000
χ29222-22-2-2-22000022-2-2-22-22i−2i−i2−i2i2i2000022-2-200000002−22i−2i00−i2−i2i2i222−2−2002i−2i0000−i2−i2i2i2000000000000002−20
χ30222-22-2-2-22000022-2-2-22-22i−2i−i2−i2i2i20000-2-22200000002−22i−2i00−i2−i2i2i222−2−200−2i2i0000i2i2−i2−i200000000000000−220
χ31222-22-2-2-22000022-2-2-22-22i−2ii2i2−i2−i2000022-2-20000000−222i−2i00i2i2−i2−i2−2−222002i−2i0000i2i2−i2−i200000000000000−220
χ32222-22-2-2-22000022-2-2-22-22i−2ii2i2−i2−i20000-2-2220000000−222i−2i00i2i2−i2−i2−2−22200−2i2i0000−i2−i2i2i2000000000000002−20
χ33222-22-2-2-22000022-2-2-22-2−2i2i−i2−i2i2i2000022-2-20000000−22−2i2i00−i2−i2i2i2−2−22200−2i2i0000−i2−i2i2i200000000000000−220
χ34222-22-2-2-22000022-2-2-22-2−2i2i−i2−i2i2i20000-2-2220000000−22−2i2i00−i2−i2i2i2−2−222002i−2i0000i2i2−i2−i2000000000000002−20
χ35222-22-2-2-22000022-2-2-22-2−2i2ii2i2−i2−i2000022-2-200000002−2−2i2i00i2i2−i2−i222−2−200−2i2i0000i2i2−i2−i2000000000000002−20
χ36222-22-2-2-22000022-2-2-22-2−2i2ii2i2−i2−i20000-2-22200000002−2−2i2i00i2i2−i2−i222−2−2002i−2i0000−i2−i2i2i200000000000000−220
χ3722-22-2-22-2222-2-22-2-222-2-2002i−2i2i−2i2-22-2000000000000000002i−2i2i−2i000000002i2i−2i−2i000000000000002-200000
χ3822-22-2-22-2222-2-22-2-222-2-2002i−2i2i−2i2-22-2000000000000000002i−2i2i−2i00000000−2i−2i2i2i00000000000000-2200000
χ3922-22-2-22-2222-2-22-2-222-2-200−2i2i−2i2i2-22-200000000000000000−2i2i−2i2i000000002i2i−2i−2i00000000000000-2200000
χ4022-22-2-22-2222-2-22-2-222-2-200−2i2i−2i2i2-22-200000000000000000−2i2i−2i2i00000000−2i−2i2i2i000000000000002-200000
χ412-22-2-222-222-22-2-2222-2-2-200000022-2-200002-2000000000000000000000002i−2i2i−2i2i−2i2i−2i02-200000000000000
χ422-22-2-222-222-22-2-2222-2-2-200000022-2-200002-200000000000000000000000−2i2i−2i2i−2i2i−2i2i02-200000000000000
χ432-22-2-222-222-22-2-2222-2-2-200000022-2-20000-22000000000000000000000002i−2i2i−2i−2i2i−2i2i0-2200000000000000
χ442-22-2-222-222-22-2-2222-2-2-200000022-2-20000-2200000000000000000000000−2i2i−2i2i2i−2i2i−2i0-2200000000000000
χ452-2-2-22-22222-2-22-2-2-22-2220000002-2-222-22-2000002-2000000000000002-2002-2-220000000002-20000000000
χ462-2-2-22-22222-2-22-2-2-22-2220000002-2-222-22-200000-22000000000000002-200-222-2000000000-220000000000
χ472-2-2-22-22222-2-22-2-2-22-2220000002-2-22-22-22000002-200000000000000-2200-222-20000000002-20000000000
χ482-2-2-22-22222-2-22-2-2-22-2220000002-2-22-22-2200000-2200000000000000-22002-2-22000000000-220000000000
χ492-2-2-22-2222-222-2-2-2-22-222000000-222-22-22-20002-20000000000000000-22000000000000000002-20002-2000
χ502-2-2-22-2222-222-2-2-2-22-222000000-222-22-22-2000-220000000000000000-2200000000000000000-22000-22000
χ512-2-2-22-2222-222-2-2-2-22-222000000-222-2-22-220002-200000000000000002-2000000000000000002-2000-22000
χ522-2-2-22-2222-222-2-2-2-22-222000000-222-2-22-22000-2200000000000000002-200000000000000000-220002-2000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-24400002222000000-4000000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000400000022-2-20000000000000000000000000000000000000
χ55444-44-4-4-4-20000-2-2222-224i−4i−2i2−2i22i22i200000000000000022−22−2i2i00i2i2−i2−i2−2−22200000000000000000000000000000
χ56444-44-4-4-4-20000-2-2222-224i−4i2i22i2−2i2−2i2000000000000000−2222−2i2i00−i2−i2i2i222−2−200000000000000000000000000000
χ57444-44-4-4-4-20000-2-2222-22−4i4i−2i2−2i22i22i2000000000000000−22222i−2i00i2i2−i2−i222−2−200000000000000000000000000000
χ58444-44-4-4-4-20000-2-2222-22−4i4i2i22i2−2i2−2i200000000000000022−222i−2i00−i2−i2i2i2−2−22200000000000000000000000000000
χ5944-44-4-44-44-4-4444-4-444-4-4000000-44-44000000000000000000000000000000000000000000000000000000
χ6044-44-4-44-4-244-4-4-222-2-222004i−4i4i−4i-22-2200000000000000000−2i2i−2i2i000000000000000000000000000000000
χ6144-44-4-44-4-244-4-4-222-2-22200−4i4i−4i4i-22-22000000000000000002i−2i2i−2i000000000000000000000000000000000
χ6244-44-4-44-4-2-4-444-222-2-2220000002-22-200000000000000000000023−2323−2300000000000000000000000000000
χ6344-44-4-44-4-2-4-444-222-2-2220000002-22-2000000000000000000000−2323−232300000000000000000000000000000
χ6444-4-4-44-44400004-44-4-4-440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ6544-4-4-44-44400004-44-4-4-4400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ6644-4-4-44-44-20000-22-2222-20022−22−2222000000000000000000023−23−222−26−6−6600000000000000000000000000000
χ6744-4-4-44-44-20000-22-2222-20022−22−22220000000000000000000−2323−222−2−666−600000000000000000000000000000
χ6844-4-4-44-44-20000-22-2222-200−222222−22000000000000000000023−232−2−22−666−600000000000000000000000000000
χ6944-4-4-44-44-20000-22-2222-200−222222−220000000000000000000−23232−2−226−6−6600000000000000000000000000000
χ704-444-4-4-4440000-44-4-44-44000000000000000000000000000000000000000000022−22−222200000000000000000
χ714-444-4-4-4440000-44-4-44-440000000000000000000000000000000000000000000−222222−2200000000000000000
χ724-44-4-444-44-44-44-4444-4-4-4000000-4-444000000000000000000000000000000000000000000000000000000
χ734-44-4-444-4-24-44-42-2-2-2222000000-2-22200004-400000000000000000000000000000000-2200000000000000
χ744-44-4-444-4-24-44-42-2-2-2222000000-2-2220000-44000000000000000000000000000000002-200000000000000
χ754-44-4-444-4-2-44-442-2-2-222200000022-2-2000000000000000000000000000000000000000023−23000000000000
χ764-44-4-444-4-2-44-442-2-2-222200000022-2-20000000000000000000000000000000000000000−2323000000000000
χ774-4-4444-4-440000-4-44-444-400000000004-4-4400000000000000000000000000000000000000000000000000
χ784-4-4444-4-440000-4-44-444-40000000000-444-400000000000000000000000000000000000000000000000000
χ794-4-4-44-444-24-4-44222-22-2-2000000-222-20000000004-40000000000000000000000000000000-220000000000
χ804-4-4-44-444-24-4-44222-22-2-2000000-222-2000000000-4400000000000000000000000000000002-20000000000
χ814-4-4-44-444-2-444-4222-22-2-20000002-2-2200000004-400000000000000000000000000000000000-2200000000
χ824-4-4-44-444-2-444-4222-22-2-20000002-2-220000000-44000000000000000000000000000000000002-200000000
χ838-888-8-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000

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