Finite Group Databasebeta

← Group #255479

Character table — Group #255479

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-111-1-1-1-1
χ91111111111-1-1-1-1111111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-111111-1-1
χ101111111111-1-1-1-1111111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-111
χ111111111111-1-1-1-1111111-1-1-1-1111111-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1111111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1111-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11111-1-11-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-111-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-111111111-1-1-1-11-1-111-1-1-111-1-111
χ1722222222222222-2-222-2-222-2-20000-2-22222-20000000000000000000000-2000000-2000000
χ1822222222222222-2-222-2-222-2-20000-2-2-2-2-2-2-2000000000000000000000020000002000000
χ192222222222-2-2-2-2-2-222-2-2-2-2220000-2-222-2-2200000000000000000000002000000-2000000
χ202222222222-2-2-2-2-2-222-2-2-2-2220000-2-2-2-22220000000000000000000000-20000002000000
χ2122222222-2-2222222-2-222-2-2222222-2-20000-2-2-222-2-2000000000000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-2-20000-222-2-222000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-200002200002000000000000000000000002-2000002-20000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-20000220000200000000000000000000000-2200000-220000
χ2522222222-2-2-2-2-2-222-2-22222-2-22222-2-200002-2-2-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2-2000022222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-2000000000000000000000002-200000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-200000000000000000000000-22000002-20000
χ2922-22-22-2-2-2-222-2-20022002-2000000002-22-20000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ3022-22-22-2-2-2-222-2-20022002-2000000002-22-20000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ3122-22-22-2-2-2-222-2-20022002-200000000-22-220000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ3222-22-22-2-2-2-222-2-20022002-200000000-22-220000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ3322-22-22-2-2-2-2-2-222002200-22000000002-2-220000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3422-22-22-2-2-2-2-2-222002200-22000000002-2-220000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ3522-22-22-2-2-2-2-2-222002200-2200000000-222-20000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ3622-22-22-2-2-2-2-2-222002200-2200000000-222-20000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-2-2-2-2222-20000222-2-2-2000022-2-22-2000002-2000000002i−2i2i−2i00000000000002i−2i0000000
χ3822-2-2-2-2222-20000222-2-2-2000022-2-22-2000002-200000000−2i2i−2i2i0000000000000−2i2i0000000
χ3922-2-2-2-2222-20000222-2-2-20000-2-2222-200000-22000000002i−2i2i−2i0000000000000−2i2i0000000
χ4022-2-2-2-2222-20000222-2-2-20000-2-2222-200000-2200000000−2i2i−2i2i00000000000002i−2i0000000
χ4122-2-2-2-222-22000022-22-2-2000022-2-2-2200000-2200002i−2i2i−2i0000000000000002i−2i000000000
χ4222-2-2-2-222-22000022-22-2-2000022-2-2-2200000-220000−2i2i−2i2i000000000000000−2i2i000000000
χ4322-2-2-2-222-22000022-22-2-20000-2-222-22000002-200002i−2i2i−2i000000000000000−2i2i000000000
χ4422-2-2-2-222-22000022-22-2-20000-2-222-22000002-20000−2i2i−2i2i0000000000000002i−2i000000000
χ452-2-222-22-2002i−2i2i−2i2-2002-2002i−2i2i−2i2i−2i0000000002-20000000000i2−i2i2−i22−22−200000000002−2i2−i2
χ462-2-222-22-2002i−2i2i−2i2-2002-2002i−2i2i−2i2i−2i0000000002-20000000000−i2i2−i2i2−22−220000000000−22−i2i2
χ472-2-222-22-2002i−2i2i−2i2-2002-2002i−2i−2i2i−2i2i000000000-220000000000i2−i2i2−i22−22−20000000000−22−i2i2
χ482-2-222-22-2002i−2i2i−2i2-2002-2002i−2i−2i2i−2i2i000000000-220000000000−i2i2−i2i2−22−2200000000002−2i2−i2
χ492-2-222-22-200−2i2i−2i2i2-2002-200−2i2i2i−2i2i−2i000000000-220000000000i2−i2i2−i2−22−2200000000002−2−i2i2
χ502-2-222-22-200−2i2i−2i2i2-2002-200−2i2i2i−2i2i−2i000000000-220000000000−i2i2−i2i22−22−20000000000−22i2−i2
χ512-2-222-22-200−2i2i−2i2i2-2002-200−2i2i−2i2i−2i2i0000000002-20000000000i2−i2i2−i2−22−220000000000−22i2−i2
χ522-2-222-22-200−2i2i−2i2i2-2002-200−2i2i−2i2i−2i2i0000000002-20000000000−i2i2−i2i22−22−200000000002−2−i2i2
χ53444-44-4-4-44-4000000-440000000000000000000000022−22−222200000000000000000000000000
χ54444-44-4-4-44-4000000-4400000000000000000000000−222222−2200000000000000000000000000
χ55444-44-4-4-4-440000004-400000000000000000000000000022−22−22220000000000000000000000
χ56444-44-4-4-4-440000004-4000000000000000000000000000−222222−220000000000000000000000
χ5744-44-44-4-44444-4-400-4-400-440000000000000000000000000000000000000000000000000
χ5844-44-44-4-444-4-44400-4-4004-40000000000000000000000000000000000000000000000000
χ5944-4-4-4-4444-40000-4-44-44400000000-4400000000000000000000000000000000000000000
χ6044-4-4-4-444-440000-4-4-4444000000004-400000000000000000000000000000000000000000
χ614-444-4-4-44004i−4i−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ624-444-4-4-44004i−4i−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ634-444-4-4-4400−4i4i4i−4i000000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ644-444-4-4-4400−4i4i4i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ654-44-4-444-40000004-400-4400004i−4i−4i4i0000000000000000000000000000000000000000000
χ664-44-4-444-40000004-400-440000−4i4i4i−4i0000000000000000000000000000000000000000000
χ674-44-4-444-4000000-44004-400000000000000000004i−4i000000000000000000000000000000
χ684-44-4-444-4000000-44004-40000000000000000000−4i4i000000000000000000000000000000
χ694-4-444-44-4004i−4i4i−4i-4400-4400−4i4i00000000000000000000000000000000000000000000000
χ704-4-444-44-400−4i4i−4i4i-4400-44004i−4i00000000000000000000000000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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