Finite Group Databasebeta

← Group #283749

Character table — Group #283749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222224444444888888888888888888881616161616161616161616161616163232
order12222244444444444442444448888888888888822244488888888828
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-11-1-11111-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-1-1-1111111111111-111-111-1-1-111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-111-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11111-1-1
χ911111111111111-1-1-1-11-1-11111-1-11111-1-1-1-11111-111-1-1-1-111-1-111-1-11-1
χ1011111111111111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1111-11111-1-1-1-1-11
χ1111111111111111-1-1-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-11111-11
χ1211111111111111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1
χ1311111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-111111111-1-11-1-1-1-1-1-111-11
χ1411111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1
χ1511111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1111111111-1-1111111-1-1-1-1-1-11-1
χ1611111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-11111111-1-1-11
χ17222222222-2-22-2-22222-2-2-222-2-222000000000000000000-20000000000
χ18222222222-2-22-2-22222-2-2-2-2-222-2-200000000000000000020000000000
χ19222222222-2-22-2-2-2-2-2-2-22222-2-2-2-200000000000000000020000000000
χ20222222222-2-22-2-2-2-2-2-2-222-2-22222000000000000000000-20000000000
χ21222222-2-2-2-2-2-22-200002000000002i2i−2i−2i00002i2i−2i−2i02-200000000000000
χ22222222-2-2-2-2-2-22-200002000000002i2i−2i−2i0000−2i−2i2i2i0-2200000000000000
χ23222222-2-2-2-2-2-22-20000200000000−2i−2i2i2i00002i2i−2i−2i0-2200000000000000
χ24222222-2-2-2-2-2-22-20000200000000−2i−2i2i2i0000−2i−2i2i2i02-200000000000000
χ252222-2-22-2-2222-2-222-2-222-2000000000000000000200-200000002-20000
χ262222-2-22-2-2222-2-222-2-222-2000000000000000000-20020000000-220000
χ272222-2-22-2-2222-2-2-2-2222-22000000000000000000200-20000000-220000
χ282222-2-22-2-2222-2-2-2-2222-22000000000000000000-200200000002-20000
χ292222-2-22-2-2-2-222222-2-2-2-22000000000000002i−2i2i−2i0000000002i−2i000000
χ302222-2-22-2-2-2-222222-2-2-2-2200000000000000−2i2i−2i2i000000000−2i2i000000
χ312222-2-22-2-2-2-2222-2-222-22-2000000000000002i−2i2i−2i000000000−2i2i000000
χ322222-2-22-2-2-2-2222-2-222-22-200000000000000−2i2i−2i2i0000000002i−2i000000
χ332222-2-2-22222-22-20000-200000000000022-2-22-2-2200002-200000000000
χ342222-2-2-22222-22-20000-200000000000022-2-2-222-20000-2200000000000
χ352222-2-2-22222-22-20000-2000000000000-2-2222-2-220000-2200000000000
χ362222-2-2-22222-22-20000-2000000000000-2-222-222-200002-200000000000
χ3722-2-22-222-200-2002i−2i2i−2i0002-2002i−2ii2−i2i2−i22−22−200000000000i2−i200002−200
χ3822-2-22-222-200-2002i−2i2i−2i0002-2002i−2i−i2i2−i2i2−22−2200000000000−i2i20000−2200
χ3922-2-22-222-200-2002i−2i2i−2i000-2200−2i2ii2−i2i2−i22−22−200000000000−i2i20000−2200
χ4022-2-22-222-200-2002i−2i2i−2i000-2200−2i2i−i2i2−i2i2−22−2200000000000i2−i200002−200
χ4122-2-22-222-200-200−2i2i−2i2i0002-200−2i2ii2−i2i2−i2−22−2200000000000i2−i20000−2200
χ4222-2-22-222-200-200−2i2i−2i2i0002-200−2i2i−i2i2−i2i22−22−200000000000−i2i200002−200
χ4322-2-22-222-200-200−2i2i−2i2i000-22002i−2ii2−i2i2−i2−22−2200000000000−i2i200002−200
χ4422-2-22-222-200-200−2i2i−2i2i000-22002i−2i−i2i2−i2i22−22−200000000000i2−i20000−2200
χ45444444-4-4-444-4-440000-40000000000000000000000000000000000000
χ464444-4-4-444-4-4-4-44000040000000000000000000000000000000000000
χ4744-4-44-4-4-4400400000000000000022−22−22220000000000000000000000000
χ4844-4-44-4-4-44004000000000000000−222222−220000000000000000000000000
χ4944-4-4-444-4400-4004i−4i−4i4i00000000000000000000000000000000000000
χ5044-4-4-444-4400-400−4i4i4i−4i00000000000000000000000000000000000000
χ5144-4-4-44-44-4004000000000000000000022−22−2222000000000000000000000
χ5244-4-4-44-44-40040000000000000000000−222222−22000000000000000000000
χ538-88-800000000000000000004-40000000000000000000000000000000
χ548-88-80000000000000000000-440000000000000000000000000000000
χ558-8-88000008-8000000000000000000000000000000000000000000000
χ568-8-8800000-88000000000000000000000000000000000000000000000

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