Finite Group Databasebeta

← Group #281771

Character table — Group #281771

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444488888888888888882244444448888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
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
χ91111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-1111111-1-1-1-111-1-1111-1
χ121111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-11111-1-11111-1-111-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-111-1-1-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-111-1-11111-1-11-1
χ17222222222-2-2-2222-222-2-2-2-22200000000000000002222-2-2-2-2-20000000000000000000000
χ18222222222-2-2-2222-222-2-2-2-2220000000000000000-2-2-2-222-2220000000000000000000000
χ19222222222-2-2-2222-2-2-222-2-2-2-2000000000000000022-2-2-2-22220000000000000000000000
χ20222222222-2-2-2222-2-2-222-2-2-2-20000000000000000-2-222222-2-20000000000000000000000
χ2122222222-2222-2-2-222222-2-2-2-22222222200000000000000-200-2-2-2-2000000000000000000
χ2222222222-2222-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000-2002222000000000000000000
χ2322222222-2222-2-2-22-2-2-2-2-2-2222222-2-2-2-200000000000000200-2-222000000000000000000
χ2422222222-2222-2-2-22-2-2-2-2-2-222-2-2-2-222220000000000000020022-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i00000020000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i0000002000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i000000-2000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i000000-20000002i2i−2i−2i00000000000000
χ2922-22-22-2-22000-2-2202-200002-2i2i2−i2−i2i2i2−i2−i222−2−222−2−200002i−2i02i−2ii2−i2i2−i22−22−200000000000000
χ3022-22-22-2-22000-2-2202-200002-2i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000−2i2i0−2i2ii2−i2i2−i2−22−2200000000000000
χ3122-22-22-2-22000-2-2202-200002-2−i2−i2i2i2−i2−i2i2i222−2−222−2−20000−2i2i0−2i2i−i2i2−i2i22−22−200000000000000
χ3222-22-22-2-22000-2-2202-200002-2−i2−i2i2i2−i2−i2i2i2−2−222−2−22200002i−2i02i−2i−i2i2−i2i2−22−2200000000000000
χ3322-22-22-2-22000-2-220-220000-22i2i2−i2−i2−i2−i2i2i222−2−222−2−20000−2i2i02i−2ii2−i2−i2i2−22−2200000000000000
χ3422-22-22-2-22000-2-220-220000-22i2i2−i2−i2−i2−i2i2i2−2−222−2−22200002i−2i0−2i2ii2−i2−i2i22−22−200000000000000
χ3522-22-22-2-22000-2-220-220000-22−i2−i2i2i2i2i2−i2−i222−2−222−2−200002i−2i0−2i2i−i2i2i2−i2−22−2200000000000000
χ3622-22-22-2-22000-2-220-220000-22−i2−i2i2i2i2i2−i2−i2−2−222−2−2220000−2i2i02i−2i−i2i2i2−i22−22−200000000000000
χ3722-22-22-2-2-200022-202-20000-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-22-200000−i2i2−i2i2i2−i2−i2i200000000000000
χ3822-22-22-2-2-200022-202-20000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-22-2200000−i2i2−i2i2−i2i2i2−i200000000000000
χ3922-22-22-2-2-200022-202-20000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-22-2200000i2−i2i2−i2i2−i2−i2i200000000000000
χ4022-22-22-2-2-200022-202-20000-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-22-200000i2−i2i2−i2−i2i2i2−i200000000000000
χ4122-22-22-2-2-200022-20-2200002-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-222-200000−i2i2i2−i2−i2i2i2−i200000000000000
χ4222-22-22-2-2-200022-20-2200002-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-2-2200000−i2i2i2−i2i2−i2−i2i200000000000000
χ4322-22-22-2-2-200022-20-2200002-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-2-2200000i2−i2−i2i2−i2i2i2−i200000000000000
χ4422-22-22-2-2-200022-20-2200002-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-222-200000i2−i2−i2i2i2−i2−i2i200000000000000
χ452-2-2-2222-2222-22-2-2-200002-200000000002i−2i2i−2i2i−2i2i−2i00000000000000000002-20000002i−2i00
χ462-2-2-2222-2222-22-2-2-200002-200000000002i−2i2i−2i2i−2i2i−2i0000000000000000000-22000000−2i2i00
χ472-2-2-2222-2222-22-2-2-200002-20000000000−2i2i−2i2i−2i2i−2i2i00000000000000000002-2000000−2i2i00
χ482-2-2-2222-2222-22-2-2-200002-20000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000-220000002i−2i00
χ492-2-2-2222-2-2-2-22-222200002-200000000002-22-2-22-22000000000000000002-20000002-20000
χ502-2-2-2222-2-2-2-22-222200002-200000000002-22-2-22-2200000000000000000-22000000-220000
χ512-2-2-2222-2-2-2-22-222200002-20000000000-22-222-22-2000000000000000002-2000000-220000
χ522-2-2-2222-2-2-2-22-222200002-20000000000-22-222-22-200000000000000000-220000002-20000
χ53444-44-4-4-404-44000-40000000000000000000000000000000000000000000000022−22000000
χ54444-44-4-4-404-44000-400000000000000000000000000000000000000000000000−2222000000
χ55444-44-4-4-40-44-400040000000000000000000000000000000000000000000002i2−2i200000000
χ56444-44-4-4-40-44-40004000000000000000000000000000000000000000000000−2i22i200000000
χ574-444-4-44-400000000004i−4i00002i2−2i22i2−2i222−2222−22000000000000000000000000000000000000000
χ584-444-4-44-400000000004i−4i0000−2i22i2−2i22i2−2222−2222000000000000000000000000000000000000000
χ594-444-4-44-40000000000−4i4i00002i2−2i22i2−2i2−2222−2222000000000000000000000000000000000000000
χ604-444-4-44-40000000000−4i4i0000−2i22i2−2i22i222−2222−22000000000000000000000000000000000000000
χ614-44-4-44-444000-44-4000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000
χ624-44-4-44-444000-44-400000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000
χ634-44-4-44-44-40004-440000000000000000022−22−2222−222222−220000000000000000000000000000000
χ644-44-4-44-44-40004-4400000000000000000−222222−2222−22−22220000000000000000000000000000000
χ654-4-444-4-4404-4-40004000000004-4-440000000000000000000000000000000000000000000
χ664-4-444-4-4404-4-4000400000000-444-40000000000000000000000000000000000000000000
χ674-4-444-4-440-444000-40000000000004i−4i−4i4i000000000000000000000000000000000000000
χ684-4-444-4-440-444000-4000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ694-4-4-4444-44-4-444-4-440000-440000000000000000000000000000000000000000000000000
χ704-4-4-4444-4-444-4-444-40000-440000000000000000000000000000000000000000000000000
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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