Finite Group Databasebeta

← Group #272267

Character table — Group #272267

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444422444444488882222444888888888822444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-111111-1-1111111-1-11-11111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-11111
χ5111111111111111-1-1-1-11111111-11111-111-1-111-1-1-1-111-11-11-1-111-1-1-1-1-11-1
χ6111111111111111-1-1-1-11111111-1-1-111-1111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-11
χ7111111111111111-1-1-1-111-1-1-1-11-11111-1-1-1-1-1-1-1111111-11-1-111-1-1-1-1-111-11
χ8111111111111111-1-1-1-111-1-1-1-11-1-1-111-1-1-111-1-11111-1-1-1-1-1-11111111-1-11-1
χ9111111111111-1-111111111111-1111-1-11-1-111111111-1-1-11-1-1-1-1111-1-111-1-1
χ10111111111111-1-111111111111-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111
χ11111111111111-1-11111111-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-11-1111-1-11-1-1-1-111
χ12111111111111-1-11111111-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-111111-11111-1-1
χ13111111111111-1-11-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1111-11111-111-1-1-11
χ14111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-1111-11-111-1-11-1-1111-1
χ15111111111111-1-11-1-1-1-111-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-11111-1-1-1-1-111111-1
χ16111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-111-1-1111-1-1-1-1-11
χ172222222-2-22-2-22220000-2-200002000-2-200000002i2i−2i−2i0000002i−2i000000000
χ182222222-2-22-2-22220000-2-200002000-2-20000000−2i−2i2i2i000000−2i2i000000000
χ192222222-2-22-2-2-2-220000-2-20000-20002200000002i2i−2i−2i000000−2i2i000000000
χ202222222-2-22-2-2-2-220000-2-20000-2000220000000−2i−2i2i2i0000002i−2i000000000
χ21222222-222-22200-22222-2-200000-22200-20022000000000-2000000-2000000
χ22222222-222-22200-22222-2-200000-2-2-200-200-2-200000000020000002000000
χ23222222-222-22200-2-2-2-2-2-2-20000022200200-2-2000000000-20000002000000
χ24222222-222-22200-2-2-2-2-2-2-2000002-2-200200220000000002000000-2000000
χ252222-2-22222-2-222-20000-222222-20002-202200-2-2000000000-200000000000
χ262222-2-22222-2-222-20000-22-2-2-2-2-20002-20-2-20022000000000200000000000
χ272222-2-22222-2-2-2-2-20000-2222222000-220-2-200-2-2000000000200000000000
χ282222-2-22222-2-2-2-2-20000-22-2-2-2-22000-220220022000000000-200000000000
χ292222-2-22-2-222222-222-2-22-20000-2200-22-200000000000020-2000000000000
χ302222-2-22-2-222222-2-2-2222-20000-2-200-222000000000000-202000000000000
χ312222-2-22-2-2222-2-2-222-2-22-2000022002-2-2000000000000-202000000000000
χ322222-2-22-2-2222-2-2-2-2-2222-200002-2002-2200000000000020-2000000000000
χ332222-2-2-2-2-2-22200222-2-2-2200000-20000200000000002-20000000002-20000
χ342222-2-2-2-2-2-22200222-2-2-2200000-2000020000000000-22000000000-220000
χ352222-2-2-2-2-2-222002-2-222-220000020000-200000000002-2000000000-220000
χ362222-2-2-2-2-2-222002-2-222-220000020000-20000000000-220000000002-20000
χ3722-2-22-202-202-20002i−2i2i−2i00i2i2−i2−i2002-2000002i−2ii2−i22−22−200000000i2−i20002−200
χ3822-2-22-202-202-20002i−2i2i−2i00i2i2−i2−i200-2200000−2i2ii2−i22−22−200000000−i2i2000−2200
χ3922-2-22-202-202-20002i−2i2i−2i00−i2−i2i2i2002-2000002i−2i−i2i2−22−2200000000−i2i2000−2200
χ4022-2-22-202-202-20002i−2i2i−2i00−i2−i2i2i200-2200000−2i2i−i2i2−22−2200000000i2−i20002−200
χ4122-2-22-202-202-2000−2i2i−2i2i00i2i2−i2−i2002-200000−2i2ii2−i2−22−2200000000i2−i2000−2200
χ4222-2-22-202-202-2000−2i2i−2i2i00i2i2−i2−i200-22000002i−2ii2−i2−22−2200000000−i2i20002−200
χ4322-2-22-202-202-2000−2i2i−2i2i00−i2−i2i2i2002-200000−2i2i−i2i22−22−200000000−i2i20002−200
χ4422-2-22-202-202-2000−2i2i−2i2i00−i2−i2i2i200-22000002i−2i−i2i22−22−200000000i2−i2000−2200
χ45444444-4-4-4-4-4-400-400004400000000000000000000000000000000000000
χ464444-4-4-444-4-4-400400004-400000000000000000000000000000000000000
χ4744-4-44-40-440-44000000000000000000000000002i2−2i2−2i22i200000000000000000
χ4844-4-44-40-440-4400000000000000000000000000−2i22i22i2−2i200000000000000000
χ4944-4-4-4404-40-440000000002i22i2−2i2−2i200000000000−2i22i2000000000000000000000
χ5044-4-4-4404-40-44000000000−2i2−2i22i22i2000000000002i2−2i2000000000000000000000
χ5144-4-4-440-4404-40004i−4i−4i4i0000000000000000000000000000000000000000
χ5244-4-4-440-4404-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ534-44-400400-4004-400000002i2−2i22i2−2i200000002i2−2i20000000000000000000000000
χ544-44-400400-4004-40000000−2i22i2−2i22i20000000−2i22i20000000000000000000000000
χ554-44-400400-400-4400000002i2−2i22i2−2i20000000−2i22i20000000000000000000000000
χ564-44-400400-400-440000000−2i22i2−2i22i200000002i2−2i20000000000000000000000000
χ578-88-800-80080000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004-4-440000000000000000000000000000000000
χ598-8-8800000000000000000-444-40000000000000000000000000000000000

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