Finite Group Databasebeta

← Group #285793

Character table — Group #285793

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444488888888888888884444444448888888844448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1111-1
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-111-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-111-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11111-1-11-1
χ17222222222-2-222-2-2222-2-222-2-20000000000000000-222-2-222-2-20000000000000000000000
χ18222222222-2-222-2-2222-2-222-2-20000000000000000-2-2-222-2-2220000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2-2-2220000000000000000222-2-2-2-2220000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-22200000000000000002-2-22222-2-20000000000000000000000
χ2122222222-222-2-222-222-2-2-2-2-2-22222-2-2-2-200000000200000000-2-222000000000000000000
χ2222222222-222-2-222-222-2-2-2-2-2-2-2-2-2-222220000000020000000022-2-2000000000000000000
χ2322222222-222-2-222-2-2-2-2-222222222222200000000-200000000-2-2-2-2000000000000000000
χ2422222222-222-2-222-2-2-2-2-22222-2-2-2-2-2-2-2-200000000-2000000002222000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222000000002i2i2i2i−2i−2i−2i−2i-20000000000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-22200000000−2i−2i−2i−2i2i2i2i2i-2000000000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i2000000000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-200000000−2i−2i−2i−2i2i2i2i2i20000000000002i2i−2i−2i00000000000000
χ2922-2-22-22-2200-2-20022-2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i202-2002-200i2−i2i2−i2i2−i2i2−i200000000000000
χ3022-2-22-22-2200-2-20022-2002-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20-2200-2200i2−i2i2−i2−i2i2−i2i200000000000000
χ3122-2-22-22-2200-2-20022-2002-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20-2200-2200−i2i2−i2i2i2−i2i2−i200000000000000
χ3222-2-22-22-2200-2-20022-2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i202-2002-200−i2i2−i2i2−i2i2−i2i200000000000000
χ3322-2-22-22-2200-2-2002-2200-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20-22002-200i2−i2−i2i2−i2i2−i2i200000000000000
χ3422-2-22-22-2200-2-2002-2200-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i202-200-2200i2−i2−i2i2i2−i2i2−i200000000000000
χ3522-2-22-22-2200-2-2002-2200-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i202-200-2200−i2i2i2−i2−i2i2−i2i200000000000000
χ3622-2-22-22-2200-2-2002-2200-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20-22002-200−i2i2i2−i2i2−i2i2−i200000000000000
χ3722-2-22-22-2-2002200-22-200-2200i2i2−i2−i2−i2−i2i2i222−2−2−2−2220002i−2i002i−2i−i2i2i2−i22−2−2200000000000000
χ3822-2-22-22-2-2002200-22-200-2200i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000−2i2i00−2i2i−i2i2i2−i2−222−200000000000000
χ3922-2-22-22-2-2002200-22-200-2200−i2−i2i2i2i2i2−i2−i222−2−2−2−222000−2i2i00−2i2ii2−i2−i2i22−2−2200000000000000
χ4022-2-22-22-2-2002200-22-200-2200−i2−i2i2i2i2i2−i2−i2−2−22222−2−20002i−2i002i−2ii2−i2−i2i2−222−200000000000000
χ4122-2-22-22-2-2002200-2-22002-200i2i2−i2−i2i2i2−i2−i222−2−2−2−222000−2i2i002i−2i−i2i2−i2i2−222−200000000000000
χ4222-2-22-22-2-2002200-2-22002-200i2i2−i2−i2i2i2−i2−i2−2−22222−2−20002i−2i00−2i2i−i2i2−i2i22−2−2200000000000000
χ4322-2-22-22-2-2002200-2-22002-200−i2−i2i2i2−i2−i2i2i222−2−2−2−2220002i−2i00−2i2ii2−i2i2−i2−222−200000000000000
χ4422-2-22-22-2-2002200-2-22002-200−i2−i2i2i2−i2−i2i2i2−2−22222−2−2000−2i2i002i−2ii2−i2i2−i22−2−2200000000000000
χ452-2-2222-2-22-2-22-222-2002-20000000000002-22-22-22-2000000000000000002i−2i0000002i−2i0000
χ462-2-2222-2-22-2-22-222-2002-20000000000002-22-22-22-200000000000000000−2i2i000000−2i2i0000
χ472-2-2222-2-22-2-22-222-2002-2000000000000-22-22-22-22000000000000000002i−2i000000−2i2i0000
χ482-2-2222-2-22-2-22-222-2002-2000000000000-22-22-22-2200000000000000000−2i2i0000002i−2i0000
χ492-2-2222-2-2-222-22-2-22002-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000002i−2i0000002-200
χ502-2-2222-2-2-222-22-2-22002-20000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000−2i2i000000-2200
χ512-2-2222-2-2-222-22-2-22002-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000002i−2i000000-2200
χ522-2-2222-2-2-222-22-2-22002-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000−2i2i0000002-200
χ534444-4-4-4-404-4004-400000000000000000000000000000000000000000000000022−22000000
χ544444-4-4-4-404-4004-4000000000000000000000000000000000000000000000000−2222000000
χ554444-4-4-4-40-4400-44000000000000000000000000000000000000000000000022−2200000000
χ564444-4-4-4-40-4400-440000000000000000000000000000000000000000000000−222200000000
χ574-44-44-4-44400-4400-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000
χ584-44-44-4-44400-4400-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000
χ594-44-44-4-44-4004-4004000000000000000022−22−2222−222222−220000000000000000000000000000000
χ604-44-44-4-44-4004-40040000000000000000−222222−2222−22−22220000000000000000000000000000000
χ614-44-4-444-4000000000000004-42i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000
χ624-44-4-444-4000000000000004-4−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000
χ634-44-4-444-400000000000000-442i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000
χ644-44-4-444-400000000000000-44−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000
χ654-4-4444-4-44444-4-4-4-400-44000000000000000000000000000000000000000000000000000
χ664-4-4444-4-4-4-4-4-4444400-44000000000000000000000000000000000000000000000000000
χ674-4-44-4-44404-400-440000000004-4-440000000000000000000000000000000000000000000
χ684-4-44-4-44404-400-44000000000-444-40000000000000000000000000000000000000000000
χ694-4-44-4-4440-44004-400000000000004-4-44000000000000000000000000000000000000000
χ704-4-44-4-4440-44004-40000000000000-444-4000000000000000000000000000000000000000
χ7188-8-8-88-88000000000000000000000000000000000000000000000000000000000000000

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