Finite Group Databasebeta

← Group #285118

Character table — Group #285118

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444888888882244488888888888844444888888888828
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11111111-1-11111111-11-1-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-11-111111-1-111-1-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ511111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-11-111-1-1-111-1-11-1-11-1
χ611111111111111111-1-1-1-11111-1-1111-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1-1111-11
χ711111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-11
χ811111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-1-111111-1-1-1-1-11-1
χ91111111111111-1-1111111111111-1-1-111111111-1-111-11-1-1-11-1-111-1-1-111-1-1
χ101111111111111-1-11111111111-1-1-1-1-11111-1-111-1-111-1-1-111-111-1-1-1-1-1-1-111
χ111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1111-1-11-1-1-1-1-1-11-1-111
χ121111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1111-11111-1-1111-1-1
χ131111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-1-1-11
χ141111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1111-11111-1-1-1-111-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111-1-1-11-1-1-1-111-1-1111111-1
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1111-1-111111-1-1-11
χ172222222-222-22-200-2-22222000022000000022-2-200000-2000-200000000000
χ182222222-222-22-200-2-222220000-2-20000000-2-2-2-2000002000200000000000
χ192222222-222-22-200-2-2-2-2-2-20000220000000-2-22200000-2000200000000000
χ202222222-222-22-200-2-2-2-2-2-20000-2-200000002222000002000-200000000000
χ21222222-22-2-22-2222-2-22i2i−2i−2i000000-2-220000002i−2i000000000000002i−2i00000
χ22222222-22-2-22-2222-2-2−2i−2i2i2i000000-2-22000000−2i2i00000000000000−2i2i00000
χ23222222-22-2-22-22-2-2-2-22i2i−2i−2i00000022-20000002i−2i00000000000000−2i2i00000
χ24222222-22-2-22-22-2-2-2-2−2i−2i2i2i00000022-2000000−2i2i000000000000002i−2i00000
χ25222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i00000002-202i−2i000000000
χ26222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i0000000-220−2i2i000000000
χ27222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i00000002-20−2i2i000000000
χ28222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i0000000-2202i−2i000000000
χ292222-2-222-2-222-2222-200002222002-2-20000000022-2-2000000000000-20000
χ302222-2-222-2-222-2222-20000-2-2-2-2002-2-200000000-2-22200000000000020000
χ312222-2-222-2-222-2-2-22-20000222200-22200000000-2-2-2-200000000000020000
χ322222-2-222-2-222-2-2-22-20000-2-2-2-200-222000000002222000000000000-20000
χ332222-2-2-22222-2-222-220000000000-22-222-2-200000000-20200000000000000
χ342222-2-2-22222-2-222-220000000000-22-2-2-2220000000020-200000000000000
χ352222-2-2-22222-2-2-2-2-2200000000002-2222-2-20000000020-200000000000000
χ362222-2-2-22222-2-2-2-2-2200000000002-22-2-22200000000-20200000000000000
χ3722-2-22-2-202-202000002i−2i2i−2ii2i2−i2−i22-20002−22−22i−2i0000i2−i200000000i2−i20002−200
χ3822-2-22-2-202-202000002i−2i2i−2ii2i2−i2−i2-220002−22−2−2i2i0000i2−i200000000−i2i2000−2200
χ3922-2-22-2-202-202000002i−2i2i−2i−i2−i2i2i22-2000−22−222i−2i0000−i2i200000000−i2i2000−2200
χ4022-2-22-2-202-202000002i−2i2i−2i−i2−i2i2i2-22000−22−22−2i2i0000−i2i200000000i2−i20002−200
χ4122-2-22-2-202-20200000−2i2i−2i2ii2i2−i2−i22-2000−22−22−2i2i0000i2−i200000000i2−i2000−2200
χ4222-2-22-2-202-20200000−2i2i−2i2ii2i2−i2−i2-22000−22−222i−2i0000i2−i200000000−i2i20002−200
χ4322-2-22-2-202-20200000−2i2i−2i2i−i2−i2i2i22-20002−22−2−2i2i0000−i2i200000000−i2i20002−200
χ4422-2-22-2-202-20200000−2i2i−2i2i−i2−i2i2i2-220002−22−22i−2i0000−i2i200000000i2−i2000−2200
χ454444-4-44-4-4-4-44400-44000000000000000000000000000000000000000000
χ464444-4-4-4-444-4-44004-4000000000000000000000000000000000000000000
χ4744-4-44-440-440-4000004-4-4400000000000000000000000000000000000000
χ4844-4-44-440-440-400000-444-400000000000000000000000000000000000000
χ4944-4-4-44404-40-400000000000000000022−22−22220000000000000000000000000
χ5044-4-4-44404-40-4000000000000000000−222222−220000000000000000000000000
χ5144-4-4-44-40-44040000000002i22i2−2i2−2i2000000000000000−2i22i200000000000000000
χ5244-4-4-44-40-4404000000000−2i2−2i22i22i20000000000000002i2−2i200000000000000000
χ534-44-4000400-4004i−4i0000002i2−2i22i2−2i2000000000000022−220000000000000000000
χ544-44-4000400-4004i−4i000000−2i22i2−2i22i20000000000000−22220000000000000000000
χ554-44-4000400-400−4i4i0000002i2−2i22i2−2i20000000000000−22220000000000000000000
χ564-44-4000400-400−4i4i000000−2i22i2−2i22i2000000000000022−220000000000000000000
χ578-88-8000-8008000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004-4-440000000000000000000000000000000000
χ598-8-8800000000000000000-444-40000000000000000000000000000000000

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