Finite Group Databasebeta

← Group #258381

Character table — Group #258381

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1111-1-11-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ711111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111111-1-1-1-111111-1-111111-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-1
χ1011111111111-1-1-1-111111-1-111111-1-1111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-1-1-111
χ1111111111111-1-1-1-111111-1-111111-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-111
χ1211111111111-1-1-1-111111-1-111111-1-1111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-111-1-11111-1-1
χ1311111111111-1-1-1-111111-1-11-1-1-1-1-1-11-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-111-1-111
χ1411111111111-1-1-1-111111-1-11-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-11111-1-1
χ1511111111111-1-1-1-111111-1-11-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-11-1-11111-1-111-1-1
χ1611111111111-1-1-1-111111-1-11-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-1-111
χ17222222222222222-2-2-2-22-2-2-2000022-200-2000022220000000000000000-2-2000000000000
χ18222222222222222-2-2-2-22-2-2-2000022-200-20000-2-2-2-2000000000000000022000000000000
χ1922222222222-2-2-2-2-2-2-2-2222-20000-2-2-2002000022-2-20000000000000000-22000000000000
χ2022222222222-2-2-2-2-2-2-2-2222-20000-2-2-20020000-2-22200000000000000002-2000000000000
χ2122222222-2-2-222222222-222-22222-2-2-2-2-2-222-2-20000000000000000000000000000000000
χ2222222222-2-2-222222222-222-2-2-2-2-2-2-2-222-2-2-2220000000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-220000-2-220020000000000000000000000000000002-22-20000
χ2422222222-2-2-22222-2-2-2-2-2-2-220000-2-22002000000000000000000000000000000-22-220000
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-22-2-2220000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-222222-2-20000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222000022200-20000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222000022200-2000000000000000000000000000000-222-20000
χ29222-2-2-2-222-2-222-2-20000200000002-2000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-2-2-222-2-222-2-20000200000002-2000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-2-2-222-2-222-2-20000200000002-200000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-2-2-222-2-222-2-20000200000002-200000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-2-2-222-2-2-2-222000020000000-22000000002i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-2-2-222-2-2-2-222000020000000-22000000002i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-2-2-222-2-2-2-222000020000000-2200000000−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-2-2-222-2-2-2-222000020000000-2200000000−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-222-2-2-20002-22-2-2-22202-202i2i−2i−2i0000002i−2i000000000000002−22−22−22−20000000000i2−i2i2−i2
χ3822-222-2-2-20002-22-2-2-22202-202i2i−2i−2i0000002i−2i00000000000000−22−22−22−220000000000−i2i2−i2i2
χ3922-222-2-2-20002-22-2-2-22202-20−2i−2i2i2i000000−2i2i000000000000002−22−22−22−20000000000−i2i2−i2i2
χ4022-222-2-2-20002-22-2-2-22202-20−2i−2i2i2i000000−2i2i00000000000000−22−22−22−220000000000i2−i2i2−i2
χ4122-222-2-2-2000-22-22-2-2220-2202i2i−2i−2i000000−2i2i000000000000002−22−2−22−220000000000i2−i2−i2i2
χ4222-222-2-2-2000-22-22-2-2220-2202i2i−2i−2i000000−2i2i00000000000000−22−222−22−20000000000−i2i2i2−i2
χ4322-222-2-2-2000-22-22-2-2220-220−2i−2i2i2i0000002i−2i000000000000002−22−2−22−220000000000−i2i2i2−i2
χ4422-222-2-2-2000-22-22-2-2220-220−2i−2i2i2i0000002i−2i00000000000000−22−222−22−20000000000i2−i2−i2i2
χ452-22-222-2-222-200002-22-2-200-22i−2i2i−2i0022i−2i00000000000002-22-20000000000002i−2i00000000
χ462-22-222-2-222-200002-22-2-200-22i−2i2i−2i0022i−2i0000000000000-22-22000000000000−2i2i00000000
χ472-22-222-2-222-200002-22-2-200-2−2i2i−2i2i002−2i2i00000000000002-22-2000000000000−2i2i00000000
χ482-22-222-2-222-200002-22-2-200-2−2i2i−2i2i002−2i2i0000000000000-22-220000000000002i−2i00000000
χ492-22-222-2-2-2-2200002-22-220022i−2i2i−2i00-2−2i2i0000000002i−2i2i−2i000000000000002-20000000000
χ502-22-222-2-2-2-2200002-22-220022i−2i2i−2i00-2−2i2i000000000−2i2i−2i2i00000000000000-220000000000
χ512-22-222-2-2-2-2200002-22-22002−2i2i−2i2i00-22i−2i0000000002i−2i2i−2i00000000000000-220000000000
χ522-22-222-2-2-2-2200002-22-22002−2i2i−2i2i00-22i−2i000000000−2i2i−2i2i000000000000002-20000000000
χ53444-4-4-4-44-44444-4-40000-40000000-44000000000000000000000000000000000000000000
χ54444-4-4-4-44-444-4-4440000-400000004-4000000000000000000000000000000000000000000
χ5544-444-4-4-40004-44-444-4-40-440000000000000000000000000000000000000000000000000
χ5644-444-4-4-4000-44-4444-4-404-40000000000000000000000000000000000000000000000000
χ5744-4-4-444-40004-4-4400000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5844-4-4-444-40004-4-440000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5944-4-4-444-4000-444-400000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ6044-4-4-444-4000-444-40000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ614-444-4-44-44-4400000000-4000000000000000000000000022−22−22220000000000000000000000
χ624-444-4-44-44-4400000000-40000000000000000000000000−222222−220000000000000000000000
χ634-444-4-44-4-44-40000000040000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ644-444-4-44-4-44-4000000004000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ654-44-444-4-444-40000-44-44-4004000000-400000000000000000000000000000000000000000
χ664-44-444-4-4-4-440000-44-44400-4000000400000000000000000000000000000000000000000
χ674-4-4-44-44400000004-4-4400000000000000004-40000000000000000000000000000000000
χ684-4-4-44-44400000004-4-440000000000000000-440000000000000000000000000000000000
χ694-4-4-44-4440000000-444-400004-4-4400000000000000000000000000000000000000000000
χ704-4-4-44-4440000000-444-40000-444-400000000000000000000000000000000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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