Finite Group Databasebeta

← Group #105120

Character table — Group #105120

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
χ9222222222222-2-2-2222-2222-2-2-2-2-2000000002222-2-2-2-20000000000000000000000
χ10222222222222-2-2-2222-2222-2-2-2-2-200000000-2-2-2-222220000000000000000000000
χ112222222222-2-222222-22-2-2-2-2-222-22222-2-2-2-2000000000000000000000000000000
χ122222222222-2-222222-22-2-2-2-2-222-2-2-2-2-22222000000000000000000000000000000
χ132222222222-2-2-2-2-222-2-2-2-2-222-2-22000000000000000000000000000000002i2i−2i−2i00
χ142222222222-2-2-2-2-222-2-2-2-2-222-2-2200000000000000000000000000000000−2i−2i2i2i00
χ1522222222-2-222222-2-2222-2-222-2-2-200000000000000000000000022-2-20000000000
χ1622222222-2-222222-2-2222-2-222-2-2-2000000000000000000000000-2-2220000000000
χ1722222222-2-222-2-2-2-2-22-22-2-2-2-22220000000000000000000000000000000000002-2
χ1822222222-2-222-2-2-2-2-22-22-2-2-2-2222000000000000000000000000000000000000-22
χ1922222222-2-2-2-2222-2-2-22-222-2-2-2-2200000000000000002i2i2i2i−2i−2i−2i−2i00000000000000
χ2022222222-2-2-2-2222-2-2-22-222-2-2-2-220000000000000000−2i−2i−2i−2i2i2i2i2i00000000000000
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
χ232222-2-2-2-2222-2000-2-220-22-2000000000000022-2-2000022−2−222−2−200002−22−2000000
χ242222-2-2-2-2222-2000-2-220-22-2000000000000022-2-20000−2−222−2−2220000−22−22000000
χ252222-2-2-2-2222-2000-2-220-22-20000000000000-2-222000022−2−222−2−20000−22−22000000
χ262222-2-2-2-2222-2000-2-220-22-20000000000000-2-2220000−2−222−2−22200002−22−2000000
χ272222-2-2-2-2-2-2-2200022-2022-20000000000000000022-2-2i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i2000000
χ282222-2-2-2-2-2-2-2200022-2022-20000000000000000022-2-2−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i2000000
χ292222-2-2-2-2-2-2-2200022-2022-200000000000000000-2-222i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i2000000
χ302222-2-2-2-2-2-2-2200022-2022-200000000000000000-2-222−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i2000000
χ3122-2-22-2-2200222-2-200-22-2002-200022−2−222−2−200000000i2−i2i2−i2i2−i2i2−i22i−2i000000000000
χ3222-2-22-2-2200222-2-200-22-2002-200022−2−222−2−200000000−i2i2−i2i2−i2i2−i2i2−2i2i000000000000
χ3322-2-22-2-2200222-2-200-22-2002-2000−2−222−2−22200000000i2−i2i2−i2i2−i2i2−i2−2i2i000000000000
χ3422-2-22-2-2200222-2-200-22-2002-2000−2−222−2−22200000000−i2i2−i2i2−i2i2−i2i22i−2i000000000000
χ3522-2-22-2-2200-2-22-2-20022200-2200022−2−2−2−222000000002−22−2−22−22002-20000000000
χ3622-2-22-2-2200-2-22-2-20022200-2200022−2−2−2−22200000000−22−222−22−200-220000000000
χ3722-2-22-2-2200-2-22-2-20022200-22000−2−22222−2−2000000002−22−2−22−2200-220000000000
χ3822-2-22-2-2200-2-22-2-20022200-22000−2−22222−2−200000000−22−222−22−2002-20000000000
χ392-22-2-2-2222-20022-22-20-2000002-2000002i−2i2i−2i2−22−22−22−20000000000000000i2−i2i2−i200
χ402-22-2-2-2222-20022-22-20-2000002-2000002i−2i2i−2i−22−22−22−220000000000000000−i2i2−i2i200
χ412-22-2-2-2222-20022-22-20-2000002-200000−2i2i−2i2i2−22−22−22−20000000000000000−i2i2−i2i200
χ422-22-2-2-2222-20022-22-20-2000002-200000−2i2i−2i2i−22−22−22−220000000000000000i2−i2i2−i200
χ432-22-2-2-2222-200-2-222-20200000-2202-22-200002−22−2−22−2200000000000000002−2−2200
χ442-22-2-2-2222-200-2-222-20200000-2202-22-20000−22−222−22−20000000000000000−222−200
χ452-22-2-2-2222-200-2-222-20200000-220-22-2200002−22−2−22−220000000000000000−222−200
χ462-22-2-2-2222-200-2-222-20200000-220-22-220000−22−222−22−200000000000000002−2−2200
χ474444-4-4-4-444-44000-4-4-404-440000000000000000000000000000000000000000000
χ484444-4-4-4-4-4-44-40004440-4-440000000000000000000000000000000000000000000
χ4944-4-44-4-440044-44400-4-4-400-4400000000000000000000000000000000000000000
χ5044-4-44-4-4400-4-4-444004-44004-400000000000000000000000000000000000000000
χ5144-4-4-444-4004-400000-404000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5244-4-4-444-4004-400000-40400000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5344-4-4-444-400-440000040-4000000000000000000000002-2-22-222-200000000000000
χ5444-4-4-444-400-440000040-400000000000000000000000-222-22-2-2200000000000000
χ554-44-444-4-44-400000-4400000000000000000022−22−222200000000000000000000000000
χ564-44-444-4-44-400000-44000000000000000000−222222−2200000000000000000000000000
χ574-44-444-4-4-44000004-4000000000000000000000022−22−22220000000000000000000000
χ584-44-444-4-4-44000004-40000000000000000000000−222222−220000000000000000000000
χ594-44-4-4-444-440044-4-440-400000-44000000000000000000000000000000000000000
χ604-44-4-4-444-4400-4-44-4404000004-4000000000000000000000000000000000000000
χ614-4-44-44-4400004-44000-40000000000002i2−2i2−2i22i2000000000000000000000000000000
χ624-4-44-44-4400004-44000-4000000000000−2i22i22i2−2i2000000000000000000000000000000
χ634-4-44-44-440000-44-400040000000022−22−22220000000000000000000000000000000000
χ644-4-44-44-440000-44-4000400000000−222222−220000000000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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