Finite Group Databasebeta

← Group #272213

Character table — Group #272213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444444488882224444888888888822444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1111111-1-111-1111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11111
χ5111111111111111-1-1111111111-1-11-111-1-111111111-1-1-1-11-1-1-1111-1-111-1-1
χ6111111111111111-1-1111111111-1-11-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111-1-11111-1-1-1-11-1-11-1111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ8111111111111111-1-11111-1-1-1-11-1-11-1-1-111-1-1-1-1-1-1-1-111-1-1-111111-11111-1-1
χ91111111111111-1-111-1-1111111-111-111111-1-111-1-1-1-111-1-111-1-111-1-1-1-1-11-1
χ101111111111111-1-111-1-1111111-111-11-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-11
χ111111111111111-1-111-1-111-1-1-1-1-111-1111-1-1-1-1-1-1111111-1-11-111-1-1-1-1-111-11
χ121111111111111-1-111-1-111-1-1-1-1-111-11-1-1-1-111-1-11111-1-1-1-1-1-11111111-1-11-1
χ131111111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-11111-111-1-1-11
χ141111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-1111-1
χ151111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-111111-1
χ161111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-11-1-1111-1-1-1-1-11
χ1722222222-2-2-2-22002200-2-200000-2-202000000002i2i−2i−2i0000002i−2i000000000
χ1822222222-2-2-2-22002200-2-200000-2-20200000000−2i−2i2i2i000000−2i2i000000000
χ1922222222-2-2-2-2200-2-200-2-200000220-2000000002i2i−2i−2i000000−2i2i000000000
χ2022222222-2-2-2-2200-2-200-2-200000220-200000000−2i−2i2i2i0000002i−2i000000000
χ21222222-2-22222-2220022-2-20000-200-202200220000000000-200000-2000000
χ22222222-2-22222-2220022-2-20000-200-20-2-200-2-200000000002000002000000
χ23222222-2-22222-2-2-200-2-2-2-20000200202200-2-20000000000-2000002000000
χ24222222-2-22222-2-2-200-2-2-2-2000020020-2-200220000000000200000-2000000
χ252222-2-22222-2-2-2002200-22222202-20-2002200-2-2000000000-200000000000
χ262222-2-22222-2-2-2002200-22-2-2-2-202-20-200-2-20022000000000200000000000
χ272222-2-22222-2-2-200-2-200-2222220-220200-2-200-2-2000000000200000000000
χ282222-2-22222-2-2-200-2-200-22-2-2-2-20-220200220022000000000-200000000000
χ292222-2-222-2-222-22222-2-22-200002-22-2-200000000000000-220000000000000
χ302222-2-222-2-222-222-2-2-2-22-2000022-2-22000000000000002-20000000000000
χ312222-2-222-2-222-2-2-222222-20000-2-222-2000000000000002-20000000000000
χ322222-2-222-2-222-2-2-2-2-2222-20000-22-22200000000000000-220000000000000
χ332222-2-2-2-2-2-22222200-2-2-220000-200200000000000002-20000000002-20000
χ342222-2-2-2-2-2-22222200-2-2-220000-20020000000000000-22000000000-220000
χ352222-2-2-2-2-2-2222-2-20022-220000200-200000000000002-2000000000-220000
χ362222-2-2-2-2-2-2222-2-20022-220000200-20000000000000-220000000002-20000
χ372-22-22-2002-22-202i−2i002i−2i00i2i2−i2−i2000002-2002i−2ii2−i22−22−200000000i2−i20002−200
χ382-22-22-2002-22-202i−2i002i−2i00i2i2−i2−i200000-2200−2i2ii2−i22−22−200000000−i2i2000−2200
χ392-22-22-2002-22-202i−2i002i−2i00−i2−i2i2i2000002-2002i−2i−i2i2−22−2200000000−i2i2000−2200
χ402-22-22-2002-22-202i−2i002i−2i00−i2−i2i2i200000-2200−2i2i−i2i2−22−2200000000i2−i20002−200
χ412-22-22-2002-22-20−2i2i00−2i2i00i2i2−i2−i2000002-200−2i2ii2−i2−22−2200000000i2−i2000−2200
χ422-22-22-2002-22-20−2i2i00−2i2i00i2i2−i2−i200000-22002i−2ii2−i2−22−2200000000−i2i20002−200
χ432-22-22-2002-22-20−2i2i00−2i2i00−i2−i2i2i2000002-200−2i2i−i2i22−22−200000000−i2i20002−200
χ442-22-22-2002-22-20−2i2i00−2i2i00−i2−i2i2i200000-22002i−2i−i2i22−22−200000000i2−i2000−2200
χ45444444-4-4-4-4-4-4-40000004400000000000000000000000000000000000000
χ464444-4-4-4-444-4-440000004-400000000000000000000000000000000000000
χ4744-4-400-4400000004i−4i00002i2−2i22i2−2i2000000022−220000000000000000000000000
χ4844-4-400-4400000004i−4i0000−2i22i2−2i22i20000000−22220000000000000000000000000
χ4944-4-400-440000000−4i4i00002i2−2i22i2−2i20000000−22220000000000000000000000000
χ5044-4-400-440000000−4i4i0000−2i22i2−2i22i2000000022−220000000000000000000000000
χ514-44-44-400-44-44000000000000000000000000002i2−2i2−2i22i200000000000000000
χ524-44-44-400-44-4400000000000000000000000000−2i22i22i2−2i200000000000000000
χ534-44-4-44004-4-440000000002i22i2−2i2−2i200000000000−2i22i2000000000000000000000
χ544-44-4-44004-4-44000000000−2i2−2i22i22i2000000000002i2−2i2000000000000000000000
χ554-44-4-4400-444-404i−4i00−4i4i0000000000000000000000000000000000000000
χ564-44-4-4400-444-40−4i4i004i−4i0000000000000000000000000000000000000000
χ5788-8-8008-8000000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004-4-440000000000000000000000000000000000
χ598-8-8800000000000000000-444-40000000000000000000000000000000000

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