Finite Group Databasebeta

← Group #252687

Character table — Group #252687

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444888888888888888822444444448888
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
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11-1-11111111111111111-1-1-1-11-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111111-111-111-1-1-1-1
χ91111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1-1-11111-1-1
χ101111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-1-111-1-111
χ111111111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1111-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-11111-1-1-1-1111111-1-1111-1-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-111111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1111-1-111
χ1722222222222222-2-222-2-222-2-20000-2-222220000-20000000000000000000000-200-2000000
χ1822222222222222-2-222-2-222-2-20000-2-2-2-2-2-20000-200000000000000000000002002000000
χ192222222222-2-2-2-2-2-222-2-2-2-2220000-2-222-2-2000020000000000000000000000-2002000000
χ202222222222-2-2-2-2-2-222-2-2-2-2220000-2-2-2-222000020000000000000000000000200-2000000
χ2122222222-2-2222222-2-222-2-2222222-2-20000-2-222-2-2-2000000000000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-2-2000022-2-2-222000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2000022000000002000000000000000000000002-202-20000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-200002200000000200000000000000000000000-220-220000
χ2522222222-2-2-2-2-2-222-2-22222-2-22222-2-20000-2-2-2-2222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2-2000022222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000-2000000000000000000000002-20-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000-200000000000000000000000-2202-20000
χ29222-2-22-2-2-2-222-2-20022002-2000000002-22-20000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-22-2-2-2-222-2-20022002-2000000002-22-20000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-22-2-2-2-222-2-20022002-200000000-22-220000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-22-2-2-2-222-2-20022002-200000000-22-220000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-22-2-2-2-2-2-222002200-22000000002-2-220000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-22-2-2-2-2-2-222002200-22000000002-2-220000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-22-2-2-2-2-2-222002200-2200000000-222-20000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-22-2-2-2-2-2-222002200-2200000000-222-20000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-2-22-22-2002i−2i2i−2i2-2002-2002i−2i2i2i−2i−2i000000002-200000000000i2−i2i2−i22−22−200000000002−2i2−i2
χ3822-2-22-22-2002i−2i2i−2i2-2002-2002i−2i2i2i−2i−2i000000002-200000000000−i2i2−i2i2−22−220000000000−22−i2i2
χ3922-2-22-22-2002i−2i2i−2i2-2002-2002i−2i−2i−2i2i2i00000000-2200000000000i2−i2i2−i22−22−20000000000−22−i2i2
χ4022-2-22-22-2002i−2i2i−2i2-2002-2002i−2i−2i−2i2i2i00000000-2200000000000−i2i2−i2i2−22−2200000000002−2i2−i2
χ4122-2-22-22-200−2i2i−2i2i2-2002-200−2i2i2i2i−2i−2i00000000-2200000000000i2−i2i2−i2−22−2200000000002−2−i2i2
χ4222-2-22-22-200−2i2i−2i2i2-2002-200−2i2i2i2i−2i−2i00000000-2200000000000−i2i2−i2i22−22−20000000000−22i2−i2
χ4322-2-22-22-200−2i2i−2i2i2-2002-200−2i2i−2i−2i2i2i000000002-200000000000i2−i2i2−i2−22−220000000000−22i2−i2
χ4422-2-22-22-200−2i2i−2i2i2-2002-200−2i2i−2i−2i2i2i000000002-200000000000−i2i2−i2i22−22−200000000002−2−i2i2
χ452-2-22-222-22-20000222-2-2-200002i−2i2i−2i2-200002i−2i0000000002i−2i2i−2i00000000002-20000000000
χ462-2-22-222-22-20000222-2-2-200002i−2i2i−2i2-200002i−2i000000000−2i2i−2i2i0000000000-220000000000
χ472-2-22-222-22-20000222-2-2-20000−2i2i−2i2i2-20000−2i2i0000000002i−2i2i−2i0000000000-220000000000
χ482-2-22-222-22-20000222-2-2-20000−2i2i−2i2i2-20000−2i2i000000000−2i2i−2i2i00000000002-20000000000
χ492-2-22-222-2-22000022-22-2-200002i−2i2i−2i-220000−2i2i000002i−2i2i−2i0000000000002-2000000000000
χ502-2-22-222-2-22000022-22-2-200002i−2i2i−2i-220000−2i2i00000−2i2i−2i2i000000000000-22000000000000
χ512-2-22-222-2-22000022-22-2-20000−2i2i−2i2i-2200002i−2i000002i−2i2i−2i000000000000-22000000000000
χ522-2-22-222-2-22000022-22-2-20000−2i2i−2i2i-2200002i−2i00000−2i2i−2i2i0000000000002-2000000000000
χ53444-4-44-4-44444-4-400-4-400-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-444-4-44400-4-4004-40000000000000000000000000000000000000000000000000
χ5544-44-4-4-44004i−4i−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ5644-44-4-4-44004i−4i−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ5744-44-4-4-4400−4i4i4i−4i000000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ5844-44-4-4-4400−4i4i4i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ5944-4-44-44-4004i−4i4i−4i-4400-4400−4i4i00000000000000000000000000000000000000000000000
χ6044-4-44-44-400−4i4i−4i4i-4400-44004i−4i00000000000000000000000000000000000000000000000
χ614-44-4-4-4440000004-400-4400004-4-440000000000000000000000000000000000000000000
χ624-44-4-4-4440000004-400-440000-444-40000000000000000000000000000000000000000000
χ634-44-4-4-444000000-44004-400000000000000000004-4000000000000000000000000000000
χ644-44-4-4-444000000-44004-40000000000000000000-44000000000000000000000000000000
χ654-4-44-444-44-40000-4-44-44400000000-4400000000000000000000000000000000000000000
χ664-4-44-444-4-440000-4-4-4444000000004-400000000000000000000000000000000000000000
χ674-4-4-444-444-4000000-440000000000000000000000022−22−222200000000000000000000000000
χ684-4-4-444-444-4000000-4400000000000000000000000−222222−2200000000000000000000000000
χ694-4-4-444-44-440000004-400000000000000000000000000022−22−22220000000000000000000000
χ704-4-4-444-44-440000004-4000000000000000000000000000−222222−220000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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