Finite Group Databasebeta

← Group #291007

Character table — Group #291007

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444222444444444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11-11-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-11-11-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ9111111111111-1-1-1-11111-1-1-1-111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1
χ10111111111111-1-1-1-11111-1-1-1-111-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-11-11
χ11111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11
χ12111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ13111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1
χ14111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-11
χ15111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-11
χ16111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-111-11-1
χ172222222222-2-2222222-2-2-2-222-2-2-222220000000000000000000000000000000000-20-2000
χ182222222222-2-2222222-2-2-2-222-2-2-2-2-2-2-20000000000000000000000000000000000202000
χ192222222222-2-2-2-2-2-222-2-222-2-2-2-2222-2-20000000000000000000000000000000000-202000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-22-2-222000000000000000000000000000000000020-2000
χ2122222222-2-2222222-2-22222-2-2-2-2-2000022220000000000000000000000000000000-20-200
χ2222222222-2-2222222-2-22222-2-2-2-2-20000-2-2-2-2000000000000000000000000000000020200
χ2322222222-2-222-2-2-2-2-2-222-2-222-2-22000022-2-2000000000000000000000000000000020-200
χ2422222222-2-222-2-2-2-2-2-222-2-222-2-220000-2-2220000000000000000000000000000000-20200
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22220000000022-2-20000000000000000000000002-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-222200000000-2-222000000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000022-2-2000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000-2-2220000000000000000000000002-2000000
χ2922-2-22-22-222-2-20000-2-22200002-20000000002i−2i2i−2i000022-2-22i2i−2i−2i00000000000000000000
χ3022-2-22-22-222-2-20000-2-22200002-20000000002i−2i2i−2i0000-2-222−2i−2i2i2i00000000000000000000
χ3122-2-22-22-222-2-20000-2-22200002-2000000000−2i2i−2i2i000022-2-2−2i−2i2i2i00000000000000000000
χ3222-2-22-22-222-2-20000-2-22200002-2000000000−2i2i−2i2i0000-2-2222i2i−2i−2i00000000000000000000
χ3322-2-22-22-2-2-222000022-2-200002-20000000002i−2i−2i2i2i2i−2i−2i0000000022-2-20000000000000000
χ3422-2-22-22-2-2-222000022-2-200002-20000000002i−2i−2i2i−2i−2i2i2i00000000-2-2220000000000000000
χ3522-2-22-22-2-2-222000022-2-200002-2000000000−2i2i2i−2i2i2i−2i−2i00000000-2-2220000000000000000
χ3622-2-22-22-2-2-222000022-2-200002-2000000000−2i2i2i−2i−2i−2i2i2i0000000022-2-20000000000000000
χ3722-2-2-22-222-2002i2i−2i−2i2-200002i−2i0002-22i−2i00000000i2−i2i2−i22−22−200000000i2i2−i2−i222−2−200000000
χ3822-2-2-22-222-2002i2i−2i−2i2-200002i−2i0002-22i−2i00000000−i2i2−i2i2−22−2200000000−i2−i2i2i2−2−22200000000
χ3922-2-2-22-222-2002i2i−2i−2i2-200002i−2i000-22−2i2i00000000i2−i2i2−i22−22−200000000−i2−i2i2i2−2−22200000000
χ4022-2-2-22-222-2002i2i−2i−2i2-200002i−2i000-22−2i2i00000000−i2i2−i2i2−22−2200000000i2i2−i2−i222−2−200000000
χ4122-2-2-22-222-200−2i−2i2i2i2-20000−2i2i0002-2−2i2i00000000i2−i2i2−i2−22−2200000000i2i2−i2−i2−2−22200000000
χ4222-2-2-22-222-200−2i−2i2i2i2-20000−2i2i0002-2−2i2i00000000−i2i2−i2i22−22−200000000−i2−i2i2i222−2−200000000
χ4322-2-2-22-222-200−2i−2i2i2i2-20000−2i2i000-222i−2i00000000i2−i2i2−i2−22−2200000000−i2−i2i2i222−2−200000000
χ4422-2-2-22-222-200−2i−2i2i2i2-20000−2i2i000-222i−2i00000000−i2i2−i2i22−22−200000000i2i2−i2−i2−2−22200000000
χ452-2-2222-2-2002-22i−2i2i−2i002-22i−2i0000000002-22i−2i0000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ462-2-2222-2-2002-22i−2i2i−2i002-22i−2i0000000002-22i−2i000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000
χ472-2-2222-2-2002-22i−2i2i−2i002-22i−2i000000000-22−2i2i0000000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ482-2-2222-2-2002-22i−2i2i−2i002-22i−2i000000000-22−2i2i000000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000
χ492-2-2222-2-2002-2−2i2i−2i2i002-2−2i2i0000000002-2−2i2i0000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ502-2-2222-2-2002-2−2i2i−2i2i002-2−2i2i0000000002-2−2i2i000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000
χ512-2-2222-2-2002-2−2i2i−2i2i002-2−2i2i000000000-222i−2i0000000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ522-2-2222-2-2002-2−2i2i−2i2i002-2−2i2i000000000-222i−2i000000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000
χ534444-4-4-4-44-4000000-44000000000000000000000000022−22−2222000000000000000000000000
χ544444-4-4-4-44-4000000-440000000000000000000000000−222222−22000000000000000000000000
χ554444-4-4-4-4-440000004-400000000000000000000022−22−22220000000000000000000000000000
χ564444-4-4-4-4-440000004-4000000000000000000000−222222−220000000000000000000000000000
χ5744-4-44-44-444440000-4-4-4-40000-44000000000000000000000000000000000000000000000
χ5844-4-44-44-4-4-4-4-4000044440000-44000000000000000000000000000000000000000000000
χ5944-4-4-44-44-44004i4i−4i−4i-440000−4i4i00000000000000000000000000000000000000000000000
χ6044-4-4-44-44-4400−4i−4i4i4i-4400004i−4i00000000000000000000000000000000000000000000000
χ614-44-44-4-44004-4000000-4400000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ624-44-44-4-44004-4000000-440000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-44-44-4-4400-440000004-40000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ644-44-44-4-4400-440000004-4000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ654-44-4-444-400004-4-440000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ664-44-4-444-400004-4-44000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ674-44-4-444-40000-444-40000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ684-44-4-444-40000-444-4000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ694-4-4444-4-400-444i−4i4i−4i00-44−4i4i0000000000000000000000000000000000000000000000000
χ704-4-4444-4-400-44−4i4i−4i4i00-444i−4i0000000000000000000000000000000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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