Finite Group Databasebeta

← Group #10828819

Character table — Group #10828819

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212222224444446688121224242424242424244444444488884121212121212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1
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
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ51111111111111111111111-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-111-1
χ911111111111111111111-1-1111111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-11
χ1011111111111111111111-1-1111111111111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-11111-1-1-111-1-1-1
χ1111111111111111111111-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-111111-1
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111
χ1311111111111111111111-1-1-1-1-1-111111111-111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11111111111-1-1-111-1-111-1-11-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111111-1-111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222-2000000-2-2002200000000-2-2220000000000000000000-200000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2000000-2-200220000000022-2-20000000000000000000200000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2222220000002200-2-200000000-2-2-2-20000000000000000000200000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000002200-2-20000000022220000000000000000000-200000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002222222-1-122-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002-2-2-2-2-2-2-1-122-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022222-2-2-1-1-2-2-1-111111111000000000000-211-1-1-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002-2-2-2-222-1-1-2-2-1-1111111110000000000002-1-11111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-222-2-2-2-211-2-211-1-1-1-111110000000000002-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2222211-2-211-1-1-1-11111000000000000-21111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-222-2-2221122111111-1-1-1-1000000000000-211-1-111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222-2-21122111111-1-1-1-10000000000002-1-111-1-11100000000
χ29222-2-2-2-222000022-2-2-22-22i−2i22−2−2000022-2-2000000000−i2i22i−2i22−2−2−i2−i2i2i2002i−2i000022−2−200000000000000−i2i20
χ30222-2-2-2-222000022-2-2-22-22i−2i22−2−20000-2-222000000000−i2i22i−2i22−2−2−i2−i2i2i200−2i2i0000−2−22200000000000000i2−i20
χ31222-2-2-2-222000022-2-2-22-22i−2i−2−222000022-2-2000000000i2−i22i−2i−2−222i2i2−i2−i2002i−2i0000−2−22200000000000000i2−i20
χ32222-2-2-2-222000022-2-2-22-22i−2i−2−2220000-2-222000000000i2−i22i−2i−2−222i2i2−i2−i200−2i2i000022−2−200000000000000−i2i20
χ33222-2-2-2-222000022-2-2-22-2−2i2i22−2−2000022-2-2000000000i2−i2−2i2i22−2−2i2i2−i2−i200−2i2i000022−2−200000000000000i2−i20
χ34222-2-2-2-222000022-2-2-22-2−2i2i22−2−20000-2-222000000000i2−i2−2i2i22−2−2i2i2−i2−i2002i−2i0000−2−22200000000000000−i2i20
χ35222-2-2-2-222000022-2-2-22-2−2i2i−2−222000022-2-2000000000−i2i2−2i2i−2−222−i2−i2i2i200−2i2i0000−2−22200000000000000−i2i20
χ36222-2-2-2-222000022-2-2-22-2−2i2i−2−2220000-2-222000000000−i2i2−2i2i−2−222−i2−i2i2i2002i−2i000022−2−200000000000000i2−i20
χ3722-22-22-2-22-22-222-2-2-22-22002-22-2-2-222000000000000000002-22-2000000002i2i−2i−2i00000000000000002i−2i000
χ3822-22-22-2-22-22-222-2-2-22-22002-22-2-2-222000000000000000002-22-200000000−2i−2i2i2i0000000000000000−2i2i000
χ3922-22-22-2-22-22-222-2-2-22-2200-22-22-2-22200000000000000000-22-22000000002i2i−2i−2i0000000000000000−2i2i000
χ4022-22-22-2-22-22-222-2-2-22-2200-22-22-2-22200000000000000000-22-2200000000−2i−2i2i2i00000000000000002i−2i000
χ412-22-222-2-22-2-222-222-2-2-220000002-22-20000000002i−2i0000000000000000002i−2i2i−2i2-22-200000002i−2i00000000
χ422-22-222-2-22-2-222-222-2-2-220000002-22-20000000002i−2i000000000000000000−2i2i−2i2i-22-2200000002i−2i00000000
χ432-22-222-2-22-2-222-222-2-2-220000002-22-2000000000−2i2i0000000000000000002i−2i2i−2i-22-220000000−2i2i00000000
χ442-22-222-2-22-2-222-222-2-2-220000002-22-2000000000−2i2i000000000000000000−2i2i−2i2i2-22-20000000−2i2i00000000
χ452-2-2-2-222222-2-22-2-2-22-222000000-222-22-22-20002-200000000000000002-2002-2-220000000002-20000000000
χ462-2-2-2-222222-2-22-2-2-22-222000000-222-22-22-2000-2200000000000000002-200-222-2000000000-220000000000
χ472-2-2-2-222222-2-22-2-2-22-222000000-222-2-22-220002-20000000000000000-2200-222-20000000002-20000000000
χ482-2-2-2-222222-2-22-2-2-22-222000000-222-2-22-22000-220000000000000000-22002-2-22000000000-220000000000
χ492-2-2-2-22222-222-2-2-2-22-2220000002-2-222-22-202-2000000000000000000-2200000000000002-200002-2000000
χ502-2-2-2-22222-222-2-2-2-22-2220000002-2-222-22-20-22000000000000000000-220000000000000-220000-22000000
χ512-2-2-2-22222-222-2-2-2-22-2220000002-2-22-22-2202-20000000000000000002-200000000000002-20000-22000000
χ522-2-2-2-22222-222-2-2-2-22-2220000002-2-22-22-220-220000000000000000002-20000000000000-2200002-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000-40000002200-2-20000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000222200004000000-2-200220000000000000000000000000000000000000
χ55444-4-4-4-44-20000-2-2222-224i−4i2222−22−2200000000000000000−2i22i2−2i2i−2−222i2i2−i2−i200000000000000000000000000000
χ56444-4-4-4-44-20000-2-2222-224i−4i−22−222222000000000000000002i2−2i2−2i2i22−2−2−i2−i2i2i200000000000000000000000000000
χ57444-4-4-4-44-20000-2-2222-22−4i4i2222−22−22000000000000000002i2−2i22i−2i−2−222−i2−i2i2i200000000000000000000000000000
χ58444-4-4-4-44-20000-2-2222-22−4i4i−22−22222200000000000000000−2i22i22i−2i22−2−2i2i2−i2−i200000000000000000000000000000
χ5944-44-44-4-444-44-44-4-4-44-4400000044-4-4000000000000000000000000000000000000000000000000000000
χ6044-44-44-4-4-24-44-4-2222-22-2000000-2-22200000000000000000000023−2323−2300000000000000000000000000000
χ6144-44-44-4-4-24-44-4-2222-22-2000000-2-222000000000000000000000−2323−232300000000000000000000000000000
χ6244-44-44-4-4-2-44-44-2222-22-2004-44-422-2-200000000000000000-22-22000000000000000000000000000000000
χ6344-44-44-4-4-2-44-44-2222-22-200-44-4422-2-2000000000000000002-22-2000000000000000000000000000000000
χ6444-4-44-44-4400004-444-4-4-40022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ6544-4-44-44-4400004-444-4-4-400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ6644-4-44-44-4-20000-22-2-22220022−22−2222000000000000000−2i32i30000−222−2i6−i6−i6i600000000000000000000000000000
χ6744-4-44-44-4-20000-22-2-22220022−22−22220000000000000002i3−2i30000−222−2−i6i6i6−i600000000000000000000000000000
χ6844-4-44-44-4-20000-22-2-222200−222222−22000000000000000−2i32i300002−2−22−i6i6i6−i600000000000000000000000000000
χ6944-4-44-44-4-20000-22-2-222200−222222−220000000000000002i3−2i300002−2−22i6−i6−i6i600000000000000000000000000000
χ704-444-4-44-440000-44-444-4-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ714-444-4-44-440000-44-444-4-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ724-44-444-4-4444-4-4-444-4-4-44000000-44-44000000000000000000000000000000000000000000000000000000
χ734-44-444-4-4-244-4-42-2-2222-20000002-22-20000000000000000000000000000000000000023−2300000000000000
χ744-44-444-4-4-244-4-42-2-2222-20000002-22-200000000000000000000000000000000000000−232300000000000000
χ754-44-444-4-4-2-4-4442-2-2222-2000000-22-220000000004i−4i000000000000000000000000000000000−2i2i00000000
χ764-44-444-4-4-2-4-4442-2-2222-2000000-22-22000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ774-4-444-4-4440000-4-44-444-400000000004-4-4400000000000000000000000000000000000000000000000000
χ784-4-444-4-4440000-4-44-444-40000000000-444-400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-24-4-44222-22-2-20000002-2-2200000004-4000000000000000000000000000000000-220000000000
χ804-4-4-4-4444-24-4-44222-22-2-20000002-2-220000000-440000000000000000000000000000000002-20000000000
χ814-4-4-4-4444-2-444-4222-22-2-2000000-222-2000004-4000000000000000000000000000000000-22000000000000
χ824-4-4-4-4444-2-444-4222-22-2-2000000-222-200000-440000000000000000000000000000000002-2000000000000
χ838-888-8-88-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000

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