Finite Group Databasebeta

← Group #285205

Character table — Group #285205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444888888882244488888888888822444888888888828
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-111-1-111-1-1111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-111-1-1-1-111-1-111-1-11111-1-1-111-1-1-1-1
χ4111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ511111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-11-1-1-1111-1-1-1-11-1
χ611111111111111111-1-1-1-11111111-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-11-1-11111-11
χ711111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111-11
χ811111111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-111-11-1-1-11111-1-11-1
χ91111111111111-1-11111111111-1-1-1111111-1-1111111-1-1-1-111-1-1-111-1-111-1-1
χ101111111111111-1-11111111111-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-111
χ111111111111111-1-1111111-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-11-1-1-1-1-1-111
χ121111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1
χ131111111111111-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111-111-11111-1-1-11
χ141111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1111-1-111111-1
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1111111-1-1-1-1-11
χ172222222-22-2-2-2222-2-22i2i−2i−2i0000-2-2200002i−2i000000000000002i−2i000000000
χ182222222-22-2-2-2222-2-2−2i−2i2i2i0000-2-220000−2i2i00000000000000−2i2i000000000
χ192222222-22-2-2-22-2-2-2-22i2i−2i−2i000022-200002i−2i00000000000000−2i2i000000000
χ202222222-22-2-2-22-2-2-2-2−2i−2i2i2i000022-20000−2i2i000000000000002i−2i000000000
χ21222222-22-2222-200-2-2222200000002200-2-2000022000000-2-200000000000
χ22222222-22-2222-200-2-222220000000-2-200-2-20000-2-20000002200000000000
χ23222222-22-2222-200-2-2-2-2-2-200000002200220000-2-2000000-2200000000000
χ24222222-22-2222-200-2-2-2-2-2-20000000-2-200220000220000002-200000000000
χ25222222-2-2-2-2-2-2-200222i2i−2i−2i00000000000−2i2i000000002-20000000002i−2i0000
χ26222222-2-2-2-2-2-2-200222i2i−2i−2i00000000000−2i2i00000000-22000000000−2i2i0000
χ27222222-2-2-2-2-2-2-20022−2i−2i2i2i000000000002i−2i000000002-2000000000−2i2i0000
χ28222222-2-2-2-2-2-2-20022−2i−2i2i2i000000000002i−2i00000000-220000000002i−2i0000
χ292222-2-2222-2-22-2222-2000000002-2-200220000-2-2000000-220000000000000
χ302222-2-2222-2-22-2222-2000000002-2-200-2-20000220000002-20000000000000
χ312222-2-2222-2-22-2-2-22-200000000-22200220000-2-20000002-20000000000000
χ322222-2-2222-2-22-2-2-22-200000000-22200-2-2000022000000-220000000000000
χ332222-2-22-2222-2-222-2200002222-22-2000000220000-2-200000000-200000000
χ342222-2-22-2222-2-222-220000-2-2-2-2-22-2000000-2-200002200000000200000000
χ352222-2-22-2222-2-2-2-2-22000022222-22000000-2-20000-2-200000000200000000
χ362222-2-22-2222-2-2-2-2-220000-2-2-2-22-220000002200002200000000-200000000
χ372-22-22-20202-2-2000002i−2i2i−2i22−2−20002-2i2−i20000i2−i22i−2i2−20000000002−200i2−i200
χ382-22-22-20202-2-2000002i−2i2i−2i22−2−2000-22i2−i20000i2−i2−2i2i2−2000000000−2200−i2i200
χ392-22-22-20202-2-2000002i−2i2i−2i−2−2220002-2−i2i20000−i2i22i−2i−22000000000−2200−i2i200
χ402-22-22-20202-2-2000002i−2i2i−2i−2−222000-22−i2i20000−i2i2−2i2i−220000000002−200i2−i200
χ412-22-22-20202-2-200000−2i2i−2i2i22−2−20002-2−i2i20000−i2i2−2i2i2−20000000002−200−i2i200
χ422-22-22-20202-2-200000−2i2i−2i2i22−2−2000-22−i2i20000−i2i22i−2i2−2000000000−2200i2−i200
χ432-22-22-20202-2-200000−2i2i−2i2i−2−2220002-2i2−i20000i2−i2−2i2i−22000000000−2200i2−i200
χ442-22-22-20202-2-200000−2i2i−2i2i−2−222000-22i2−i20000i2−i22i−2i−220000000002−200−i2i200
χ454444-4-4-44-4-4-44400-44000000000000000000000000000000000000000000
χ464444-4-4-4-4-444-44004-4000000000000000000000000000000000000000000
χ4744-4-40040-400004i−4i00000022−2222−220000000002i2−2i200000000000000000000000
χ4844-4-40040-400004i−4i000000−2222−2222000000000−2i22i200000000000000000000000
χ4944-4-40040-40000−4i4i00000022−2222−22000000000−2i22i200000000000000000000000
χ5044-4-40040-40000−4i4i000000−2222−22220000000002i2−2i200000000000000000000000
χ514-44-44-40-40-444000004-4-4400000000000000000000000000000000000000
χ524-44-44-40-40-44400000-444-400000000000000000000000000000000000000
χ534-44-4-44040-44-40000000000000000002i2−2i20000−2i22i2000000000000000000000
χ544-44-4-44040-44-4000000000000000000−2i22i200002i2−2i2000000000000000000000
χ554-44-4-440-404-440000000002222−22−22000000000000000−222200000000000000000
χ564-44-4-440-404-44000000000−22−22222200000000000000022−2200000000000000000
χ5788-8-800-80800000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004-4-440000000000000000000000000000000000
χ598-8-8800000000000000000-444-40000000000000000000000000000000000

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