Finite Group Databasebeta

← Group #105132

Character table — Group #105132

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ92222222222222-2-222-22-22-2-2-2-22-22222-2-2-2-2000000000000000000000000000000
χ102222222222222-2-222-22-22-2-2-2-22-2-2-2-2-22222000000000000000000000000000000
χ1122222222222-2-222-2-2222-222-2-2-2-200000000000000000000000022-2-20000000000
χ1222222222222-2-222-2-2222-222-2-2-2-2000000000000000000000000-2-2220000000000
χ1322222222222-2-2-2-2-2-2-22-2-2-2-222-2200000000000000002i2i2i2i−2i−2i−2i−2i00000000000000
χ1422222222222-2-2-2-2-2-2-22-2-2-2-222-220000000000000000−2i−2i−2i−2i2i2i2i2i00000000000000
χ1522222222-2-2-22222222-22-2-2-222-2-2000000002222-2-2-2-20000000000000000000000
χ1622222222-2-2-22222222-22-2-2-222-2-200000000-2-2-2-222220000000000000000000000
χ1722222222-2-2-222-2-222-2-2-2-222-2-2-22000000000000000000000000000000002i2i−2i−2i00
χ1822222222-2-2-222-2-222-2-2-2-222-2-2-2200000000000000000000000000000000−2i−2i2i2i00
χ1922222222-2-2-2-2-222-2-22-222-2-2-2-2220000000000000000000000000000000000002-2
χ2022222222-2-2-2-2-222-2-22-222-2-2-2-222000000000000000000000000000000000000-22
χ2122222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000000000000000000000002i2i−2i−2i000000
χ2222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000000000000000−2i−2i2i2i000000
χ232222-2-2-2-222-22-2002-20-2020000-20000022-2-222−2−222−2−200000000000000002−22−200
χ242222-2-2-2-222-22-2002-20-2020000-20000022-2-2−2−222−2−2220000000000000000−22−2200
χ252222-2-2-2-222-22-2002-20-2020000-200000-2-22222−2−222−2−20000000000000000−22−2200
χ262222-2-2-2-222-22-2002-20-2020000-200000-2-222−2−222−2−22200000000000000002−22−200
χ272222-2-2-2-2-2-222-2002-2020-20000202i2i−2i−2i000022−2−2−2−2220000000000000000i2−i2−i2i200
χ282222-2-2-2-2-2-222-2002-2020-20000202i2i−2i−2i0000−2−22222−2−20000000000000000−i2i2i2−i200
χ292222-2-2-2-2-2-222-2002-2020-2000020−2i−2i2i2i000022−2−2−2−2220000000000000000−i2i2i2−i200
χ302222-2-2-2-2-2-222-2002-2020-2000020−2i−2i2i2i0000−2−22222−2−20000000000000000i2−i2−i2i200
χ3122-2-22-22-22-22002200-2-2-202-200002−22−22−22−20000000022−2−222−2−22-2000000000000
χ3222-2-22-22-22-22002200-2-2-202-200002−22−22−22−200000000−2−222−2−222-22000000000000
χ3322-2-22-22-22-22002200-2-2-202-20000−22−22−22−220000000022−2−222−2−2-22000000000000
χ3422-2-22-22-22-22002200-2-2-202-20000−22−22−22−2200000000−2−222−2−2222-2000000000000
χ3522-2-22-22-22-2200-2-2002-220-2200002−22−2−22−2200000000i2i2−i2−i2−i2−i2i2i2002i−2i0000000000
χ3622-2-22-22-22-2200-2-2002-220-2200002−22−2−22−2200000000−i2−i2i2i2i2i2−i2−i200−2i2i0000000000
χ3722-2-22-22-22-2200-2-2002-220-220000−22−222−22−200000000i2i2−i2−i2−i2−i2i2i200−2i2i0000000000
χ3822-2-22-22-22-2200-2-2002-220-220000−22−222−22−200000000−i2−i2i2i2i2i2−i2−i2002i−2i0000000000
χ392-22-2-2-222000222-2-2-220-20002-200000000002-22-20000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2000000
χ402-22-2-2-222000222-2-2-220-20002-200000000002-22-20000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2000000
χ412-22-2-2-222000222-2-2-220-20002-20000000000-22-220000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2000000
χ422-22-2-2-222000222-2-2-220-20002-20000000000-22-220000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2000000
χ432-22-2-2-222000-2-2-2222-2020002-2000000000000002-22-22−22−2−22−2200002−2−22000000
χ442-22-2-2-222000-2-2-2222-2020002-2000000000000002-22-2−22−222−22−20000−222−2000000
χ452-22-2-2-222000-2-2-2222-2020002-200000000000000-22-222−22−2−22−220000−222−2000000
χ462-22-2-2-222000-2-2-2222-2020002-200000000000000-22-22−22−222−22−200002−2−22000000
χ474444-4-4-4-444-4-4400-440-40-400004000000000000000000000000000000000000000
χ484444-4-4-4-4-4-44-4400-4404040000-4000000000000000000000000000000000000000
χ4944-4-44-44-4-44-4004400-44-40-44000000000000000000000000000000000000000000
χ5044-4-44-44-4-44-400-4-40044404-4000000000000000000000000000000000000000000
χ5144-4-4-44-444-4-40000000400000000000022−22−2222000000000000000000000000000000
χ5244-4-4-44-444-4-400000004000000000000−222222−22000000000000000000000000000000
χ5344-4-4-44-44-4440000000-4000000002i2−2i2−2i22i20000000000000000000000000000000000
χ5444-4-4-44-44-4440000000-400000000−2i22i22i2−2i20000000000000000000000000000000000
χ554-44-444-4-40004-400-4400000000000000000022−22−222200000000000000000000000000
χ564-44-444-4-40004-400-44000000000000000000−222222−2200000000000000000000000000
χ574-44-444-4-4000-44004-4000000000000000000000022−22−22220000000000000000000000
χ584-44-444-4-4000-44004-40000000000000000000000−222222−220000000000000000000000
χ594-44-4-4-44400044-44-4-4-404000-440000000000000000000000000000000000000000
χ604-44-4-4-444000-4-44-44440-4000-440000000000000000000000000000000000000000
χ614-4-44-444-4000004-400-404000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ624-4-44-444-4000004-400-40400000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ634-4-44-444-400000-440040-4000000000000000000000002-2-22-222-200000000000000
χ644-4-44-444-400000-440040-400000000000000000000000-222-22-2-2200000000000000
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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