Finite Group Databasebeta

← Group #258317

Character table — Group #258317

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422224444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1
χ911111111111-1-1-1-111111-1-11-1-11111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-1
χ1011111111111-1-1-1-111111-1-11-1-11111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-1-1-111
χ1111111111111-1-1-1-111111-1-11-1-111111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-111
χ1211111111111-1-1-1-111111-1-11-1-111111-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-11111-1-1
χ1311111111111-1-1-1-111111-1-11-1-1-1-1-1-1111-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-111
χ1411111111111-1-1-1-111111-1-11-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-11111-1-1-1-1111111-1-11-1-1-11111-1-1
χ1511111111111-1-1-1-111111-1-11-1-1-1-1-1-11-1-111-1-11111-11111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1
χ1611111111111-1-1-1-111111-1-11-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-111111111-1-1-1-111-1-1-1111-1-1-1-111
χ17222222222222222-2-2-2-2222-2-2-20000-22222000000-200000000000000000000-2-200000000
χ18222222222222222-2-2-2-2222-2-2-20000-2-2-2-2-2000000-2000000000000000000002200000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2-2220000-222-2-2000000200000000000000000000-2200000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2220000-2-2-2220000002000000000000000000002-200000000
χ2122222222-2-2-222222222-2-2-2-2222222-20000-2-222-2-2-2000000000000000000000000000000
χ2222222222-2-2-222222222-2-2-2-222-2-2-2-2-2000022-2-222-2000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-22-2-2000020000000000200000000000000000000002-22-20000
χ2422222222-2-2-22222-2-2-2-2-2-2-22-2-200002000000000020000000000000000000000-22-220000
χ2522222222-2-2-2-2-2-2-22222-222-2-2-22222-20000-2-2-2-2222000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-222-2-2-2-2-2-2-2-200002222-2-22000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222000020000000000-200000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222000020000000000-20000000000000000000000-222-20000
χ29222-2-22-2-22-2-222-2-2000022-2000000002-22-20000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-22-2-22-2-222-2-2000022-2000000002-22-20000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-22-2-22-2-222-2-2000022-200000000-22-220000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-22-2-22-2-222-2-2000022-200000000-22-220000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-22-2-22-2-2-2-22200002-22000000002-2-220000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-22-2-22-2-2-2-22200002-22000000002-2-220000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-22-2-22-2-2-2-22200002-2200000000-222-20000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-22-2-22-2-2-2-22200002-2200000000-222-20000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-22-2-22-222-200002-22-2-200-2002i2i−2i−2i200002i−2i0000000002-22-200000000002i−2i0000000000
χ3822-22-2-22-222-200002-22-2-200-2002i2i−2i−2i200002i−2i000000000-22-220000000000−2i2i0000000000
χ3922-22-2-22-222-200002-22-2-200-200−2i−2i2i2i20000−2i2i0000000002-22-20000000000−2i2i0000000000
χ4022-22-2-22-222-200002-22-2-200-200−2i−2i2i2i20000−2i2i000000000-22-2200000000002i−2i0000000000
χ4122-22-2-22-2-2-2200002-22-22002002i2i−2i−2i-20000−2i2i000002i−2i2i−2i0000000000002-2000000000000
χ4222-22-2-22-2-2-2200002-22-22002002i2i−2i−2i-20000−2i2i00000−2i2i−2i2i000000000000-22000000000000
χ4322-22-2-22-2-2-2200002-22-2200200−2i−2i2i2i-200002i−2i000002i−2i2i−2i000000000000-22000000000000
χ4422-22-2-22-2-2-2200002-22-2200200−2i−2i2i2i-200002i−2i00000−2i2i−2i2i0000000000002-2000000000000
χ452-2-2-2222-20002-22-222-2-200002-22i−2i2i−2i00000002i−2i00000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ462-2-2-2222-20002-22-222-2-200002-22i−2i2i−2i00000002i−2i00000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ472-2-2-2222-20002-22-222-2-200002-2−2i2i−2i2i0000000−2i2i00000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ482-2-2-2222-20002-22-222-2-200002-2−2i2i−2i2i0000000−2i2i00000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ492-2-2-2222-2000-22-2222-2-20000-222i−2i2i−2i0000000−2i2i00000000000i2−i2i2−i2−i2i2−i2i200000000002−2−22
χ502-2-2-2222-2000-22-2222-2-20000-222i−2i2i−2i0000000−2i2i00000000000−i2i2−i2i2i2−i2i2−i20000000000−222−2
χ512-2-2-2222-2000-22-2222-2-20000-22−2i2i−2i2i00000002i−2i00000000000i2−i2i2−i2−i2i2−i2i20000000000−222−2
χ522-2-2-2222-2000-22-2222-2-20000-22−2i2i−2i2i00000002i−2i00000000000−i2i2−i2i2i2−i2i2−i200000000002−2−22
χ53444-4-44-4-4-44444-4-40000-4-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-444-4-4440000-44-40000000000000000000000000000000000000000000000000
χ5544-44-4-44-444-40000-44-44-4004000000-400000000000000000000000000000000000000000
χ5644-44-4-44-4-4-440000-44-44400-4000000400000000000000000000000000000000000000000
χ5744-4-44-4-444-4400000000-400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5844-4-44-4-444-4400000000-40000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5944-4-44-4-44-44-400000000400000000000000000000022−22−222200000000000000000000000000
χ6044-4-44-4-44-44-4000000004000000000000000000000−222222−2200000000000000000000000000
χ614-44-4-4-44400000004-4-440000004-4-44000000000000000000000000000000000000000000
χ624-44-4-4-44400000004-4-44000000-444-4000000000000000000000000000000000000000000
χ634-44-4-4-4440000000-444-400000000000000000004-40000000000000000000000000000000
χ644-44-4-4-4440000000-444-40000000000000000000-440000000000000000000000000000000
χ654-4-44-44-440004-4-4400000000000000000000000000000000002-2-222-2-2200000000000000
χ664-4-44-44-440004-4-440000000000000000000000000000000000-222-2-222-200000000000000
χ674-4-44-44-44000-444-400000000000000000000000000000000002-2-22-222-200000000000000
χ684-4-44-44-44000-444-40000000000000000000000000000000000-222-22-2-2200000000000000
χ694-4-4-4444-40004-44-4-4-4440000-440000000000000000000000000000000000000000000000
χ704-4-4-4444-4000-44-44-4-44400004-40000000000000000000000000000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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