Finite Group Databasebeta

← Group #272215

Character table — Group #272215

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444422444444488882244444888888888844444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-111111111-1-1-1111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-11111
χ5111111111111111-1-1-1-11111111-111-11111-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-11-1
χ6111111111111111-1-1-1-11111111-111-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-11
χ7111111111111111-1-1-1-111-1-1-1-11-111-111-1-1-1-1-1-11111-1-1111-111-1-1-1-1-111-11
χ8111111111111111-1-1-1-111-1-1-1-11-111-1-1-1-1-111-1-11111-1-1-1-1-1-11111111-1-11-1
χ9111111111111-1-111111111111-11-1-1111-1-111111111-1-11-1-1-1-1-1111-1-111-1-1
χ10111111111111-1-111111111111-11-1-11-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-1-111
χ11111111111111-1-11111111-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-11-1-1111-1-11-1-1-1-111
χ12111111111111-1-11111111-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11111111-11111-1-1
χ13111111111111-1-11-1-1-1-1111111-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-11111-111-1-1-11
χ14111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-11-1-1111-1
χ15111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-1-111111-1
χ16111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1111-1-1111-1-1-1-1-11
χ1722222222-2-2-2-22220000-2-2000020-2-20000000002i2i−2i−2i0000002i−2i000000000
χ1822222222-2-2-2-22220000-2-2000020-2-2000000000−2i−2i2i2i000000−2i2i000000000
χ1922222222-2-2-2-2-2-220000-2-20000-20220000000002i2i−2i−2i000000−2i2i000000000
χ2022222222-2-2-2-2-2-220000-2-20000-2022000000000−2i−2i2i2i0000002i−2i000000000
χ21222222-2-2222200-22222-2-200000-200-222002200000000-20000000-2000000
χ22222222-2-2222200-22222-2-200000-200-2-2-200-2-200000000200000002000000
χ23222222-2-2222200-2-2-2-2-2-2-20000020022200-2-200000000-200000002000000
χ24222222-2-2222200-2-2-2-2-2-2-2000002002-2-200220000000020000000-2000000
χ252222-2-22222-2-222-20000-222222-202-20002200-2-2000000000-200000000000
χ262222-2-22222-2-222-20000-22-2-2-2-2-202-2000-2-20022000000000200000000000
χ272222-2-22222-2-2-2-2-20000-22222220-22000-2-200-2-2000000000200000000000
χ282222-2-22222-2-2-2-2-20000-22-2-2-2-220-22000220022000000000-200000000000
χ292222-2-222-2-22222-222-2-22-20000-22-22-20000000000002-2000000000000000
χ302222-2-222-2-22222-2-2-2222-20000-2-2-222000000000000-22000000000000000
χ312222-2-222-2-222-2-2-222-2-22-20000222-2-2000000000000-22000000000000000
χ322222-2-222-2-222-2-2-2-2-2222-200002-22-220000000000002-2000000000000000
χ332222-2-2-2-2-2-22200222-2-2-2200000-20020000000000000002-20000002-20000
χ342222-2-2-2-2-2-22200222-2-2-2200000-2002000000000000000-22000000-220000
χ352222-2-2-2-2-2-222002-2-222-2200000200-20000000000000002-2000000-220000
χ362222-2-2-2-2-2-222002-2-222-2200000200-2000000000000000-220000002-20000
χ372-22-22-2002-22-20002i−2i2i−2i00i2i2−i2−i2000002i−2i002-2i2−i22−22−2000000002−2000i2−i200
χ382-22-22-2002-22-20002i−2i2i−2i00i2i2−i2−i200000−2i2i00-22i2−i22−22−200000000−22000−i2i200
χ392-22-22-2002-22-20002i−2i2i−2i00−i2−i2i2i2000002i−2i002-2−i2i2−22−2200000000−22000−i2i200
χ402-22-22-2002-22-20002i−2i2i−2i00−i2−i2i2i200000−2i2i00-22−i2i2−22−22000000002−2000i2−i200
χ412-22-22-2002-22-2000−2i2i−2i2i00i2i2−i2−i2000002i−2i00-22i2−i2−22−22000000002−2000−i2i200
χ422-22-22-2002-22-2000−2i2i−2i2i00i2i2−i2−i200000−2i2i002-2i2−i2−22−2200000000−22000i2−i200
χ432-22-22-2002-22-2000−2i2i−2i2i00−i2−i2i2i2000002i−2i00-22−i2i22−22−200000000−22000i2−i200
χ442-22-22-2002-22-2000−2i2i−2i2i00−i2−i2i2i200000−2i2i002-2−i2i22−22−2000000002−2000−i2i200
χ45444444-4-4-4-4-4-400-400004400000000000000000000000000000000000000
χ464444-4-4-4-444-4-400400004-400000000000000000000000000000000000000
χ4744-4-4004-400004-4000000022−2222−22000000022−220000000000000000000000000
χ4844-4-4004-400004-40000000−2222−22220000000−22220000000000000000000000000
χ4944-4-4004-40000-44000000022−2222−220000000−22220000000000000000000000000
χ5044-4-4004-40000-440000000−2222−2222000000022−220000000000000000000000000
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
χ554-44-4-4400-444-40004i−4i−4i4i0000000000000000000000000000000000000000
χ564-44-4-4400-444-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ5788-8-800-88000000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ598-8-8800000000000000000−4i4i4i−4i0000000000000000000000000000000000

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