Finite Group Databasebeta

← Group #174037

Character table — Group #174037

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222222244444444444444444444444444488888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111-1-111-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ511111111111111111111111111-1-111-1-111-1-11-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1
χ611111111111111111111111111-1-111-1-111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-11-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-111-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ172222222222222222-2-2-2-22-2-2-22-20022002200-2000000000000000000000000000-20-20000
χ182222222222222222-2-2-2-22-2-2-22-200-2-200-2-200-20000000000000000000000000002020000
χ19222222222222-2-2-2-22222-22-2-2-222200220000-200000000000000000000000000-20-200000
χ20222222222222-2-2-2-22222-22-2-2-22-2-200-2-20000-20000000000000000000000000020200000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-200000000222-2-200000000000000000000000000002-200
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-200000000-2-22220000000000000000000000000000-2200
χ2322222222-2-2-2-222222222-2-222-2-20000000022-2220000000000000000000000000000-2-200
χ2422222222-2-2-2-222222222-2-222-2-200000000-2-2-2-2-200000000000000000000000000002200
χ2522222222-2-2-2-22222-2-2-2-2-22-2-2-222200-2-20000200000000000000000000000000-20200000
χ2622222222-2-2-2-22222-2-2-2-2-22-2-2-22-2-20022000020000000000000000000000000020-200000
χ2722222222-2-2-2-2-2-2-2-222222-2-2-22-2002200-2-2002000000000000000000000000000-2020000
χ2822222222-2-2-2-2-2-2-2-222222-2-2-22-200-2-2002200200000000000000000000000000020-20000
χ29222-2-2-2-2200002i2i−2i−2i2i2i−2i−2i002-200000000002i−2i02-200000000i2i2−i2−i222−2−2i2i2−i2−i222−2−200000000
χ30222-2-2-2-2200002i2i−2i−2i2i2i−2i−2i002-200000000002i−2i02-200000000−i2−i2i2i2−2−222−i2−i2i2i2−2−22200000000
χ31222-2-2-2-2200002i2i−2i−2i2i2i−2i−2i002-20000000000−2i2i0-2200000000i2i2−i2−i222−2−2−i2−i2i2i2−2−22200000000
χ32222-2-2-2-2200002i2i−2i−2i2i2i−2i−2i002-20000000000−2i2i0-2200000000−i2−i2i2i2−2−222i2i2−i2−i222−2−200000000
χ33222-2-2-2-220000−2i−2i2i2i−2i−2i2i2i002-200000000002i−2i0-2200000000i2i2−i2−i2−2−222−i2−i2i2i222−2−200000000
χ34222-2-2-2-220000−2i−2i2i2i−2i−2i2i2i002-200000000002i−2i0-2200000000−i2−i2i2i222−2−2i2i2−i2−i2−2−22200000000
χ35222-2-2-2-220000−2i−2i2i2i−2i−2i2i2i002-20000000000−2i2i02-200000000i2i2−i2−i2−2−222i2i2−i2−i2−2−22200000000
χ36222-2-2-2-220000−2i−2i2i2i−2i−2i2i2i002-20000000000−2i2i02-200000000−i2−i2i2i222−2−2−i2−i2i2i222−2−200000000
χ3722-222-2-2-222-2-200002-22-20-200022i−2i002i−2i000000022−2−222−2−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-222-2-2-222-2-200002-22-20-200022i−2i002i−2i0000000−2−222−2−222−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-222-2-2-222-2-200002-22-20-20002−2i2i00−2i2i000000022−2−222−2−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4022-222-2-2-222-2-200002-22-20-20002−2i2i00−2i2i0000000−2−222−2−222i2−i2i2−i2i2−i2i2−i20000000000000000
χ4122-222-2-2-2-2-2220000-22-220-200022i−2i00−2i2i000000022−2−2−2−222i2−i2i2−i2−i2i2−i2i20000000000000000
χ4222-222-2-2-2-2-2220000-22-220-200022i−2i00−2i2i0000000−2−22222−2−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4322-222-2-2-2-2-2220000-22-220-20002−2i2i002i−2i000000022−2−2−2−222−i2i2−i2i2i2−i2i2−i20000000000000000
χ4422-222-2-2-2-2-2220000-22-220-20002−2i2i002i−2i0000000−2−22222−2−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ452-222-22-2-22-22-22-22-20000-200020002i−2i002i−2i000002−22−22−22−200000000i2−i2i2−i2i2−i2i2−i200000000
χ462-222-22-2-22-22-22-22-20000-200020002i−2i002i−2i00000−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i200000000
χ472-222-22-2-22-22-22-22-20000-20002000−2i2i00−2i2i000002−22−22−22−200000000−i2i2−i2i2−i2i2−i2i200000000
χ482-222-22-2-22-22-22-22-20000-20002000−2i2i00−2i2i00000−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i200000000
χ492-222-22-2-2-22-22-22-220000-200020002i−2i00−2i2i000002−22−2−22−2200000000i2−i2i2−i2−i2i2−i2i200000000
χ502-222-22-2-2-22-22-22-220000-200020002i−2i00−2i2i00000−22−222−22−200000000−i2i2−i2i2i2−i2i2−i200000000
χ512-222-22-2-2-22-22-22-220000-20002000−2i2i002i−2i000002−22−2−22−2200000000−i2i2−i2i2i2−i2i2−i200000000
χ522-222-22-2-2-22-22-22-220000-20002000−2i2i002i−2i00000−22−222−22−200000000i2−i2i2−i2−i2i2−i2i200000000
χ53444-4-4-4-4400004i4i−4i−4i−4i−4i4i4i00-4400000000000000000000000000000000000000000000000
χ54444-4-4-4-440000−4i−4i4i4i4i4i−4i−4i00-4400000000000000000000000000000000000000000000000
χ5544-444-4-4-444-4-40000-44-4404000-4000000000000000000000000000000000000000000000
χ5644-444-4-4-4-4-44400004-44-404000-4000000000000000000000000000000000000000000000
χ5744-4-4-444-4000000004i−4i−4i4i0000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5844-4-4-444-4000000004i−4i−4i4i000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ5944-4-4-444-400000000−4i4i4i−4i0000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ6044-4-4-444-400000000−4i4i4i−4i000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ614-444-44-4-44-44-4-44-4400004000-40000000000000000000000000000000000000000000000
χ624-444-44-4-4-44-444-44-400004000-40000000000000000000000000000000000000000000000
χ634-44-44-44-400004i−4i−4i4i0000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ644-44-44-44-400004i−4i−4i4i000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ654-44-44-44-40000−4i4i4i−4i0000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ664-44-44-44-40000−4i4i4i−4i000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ674-4-44-4-4444-4-440000000000000000000000000002-2-222-2-22000000000000000000000000
χ684-4-44-4-4444-4-44000000000000000000000000000-222-2-222-2000000000000000000000000
χ694-4-44-4-444-444-40000000000000000000000000002-2-22-222-2000000000000000000000000
χ704-4-44-4-444-444-4000000000000000000000000000-222-22-2-22000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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