Finite Group Databasebeta

← Group #284880

Character table — Group #284880

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222244444444444444444448888888888888888888888161616161616161616323232
order12222244444422444448888888888882244448888888888888888222444888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1111-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1-11
χ61111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ9111111111111-1-111-1-11111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111-1-11111-1-1-11-1
χ10111111111111-1-111-1-11111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-111-1-1-1-1111-11
χ11111111111111-1-111-1-1111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11-1-11-1-11-1-11-11
χ12111111111111-1-111-1-1111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-111-111-111-11-1
χ13111111111111-1-111-1-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-111-1111-1-11-1-1
χ14111111111111-1-111-1-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-11-1-1-111-111
χ15111111111111-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-11-1-1-111
χ16111111111111-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1111-1111-1-1
χ1722222222-22-2222-2-222-200000000000022-2-2-2-2-2-200220000000000000000000000
χ1822222222-22-2222-2-222-2000000000000-2-2-2-2222200-2-20000000000000000000000
χ1922222222-22-22-2-2-2-2-2-2-20000000000002222-2-22200-2-20000000000000000000000
χ2022222222-22-22-2-2-2-2-2-2-2000000000000-2-22222-2-200220000000000000000000000
χ21222222-2-2-2-2-2-2002-20022i2i−2i−2i2i2i−2i−2i0000000000000000000000000002-200002i−2i000
χ22222222-2-2-2-2-2-2002-20022i2i−2i−2i2i2i−2i−2i000000000000000000000000000-220000−2i2i000
χ23222222-2-2-2-2-2-2002-2002−2i−2i2i2i−2i−2i2i2i0000000000000000000000000002-20000−2i2i000
χ24222222-2-2-2-2-2-2002-2002−2i−2i2i2i−2i−2i2i2i000000000000000000000000000-2200002i−2i000
χ252222-2-22-22-222002-200-22222-2-2-2-200000000000000000000002200-200200-200000
χ262222-2-22-22-222002-200-22222-2-2-2-20000000000000000000000-2-200200-200200000
χ272222-2-22-22-222002-200-2-2-2-2-2222200000000000000000000002200200-200-200000
χ282222-2-22-22-222002-200-2-2-2-2-222220000000000000000000000-2-200-200200200000
χ292222-2-2-22222-222-2-2-2-2200000000222200-220000-2-20000002200-2-2000000000000
χ302222-2-2-22222-222-2-2-2-2200000000-2-2-2-200-22000022000000-2-20022000000000000
χ312222-2-2-22222-2-2-2-2-2222000000002222002-2000022000000-2-200-2-2000000000000
χ322222-2-2-22222-2-2-2-2-222200000000-2-2-2-2002-20000-2-2000000220022000000000000
χ332222-2-2-22-22-2-22222-2-2-22i2i−2i−2i−2i−2i2i2i0000002-2000000002i2i−2i−2i000000000000000000
χ342222-2-2-22-22-2-22222-2-2-2−2i−2i2i2i2i2i−2i−2i0000002-200000000−2i−2i2i2i000000000000000000
χ352222-2-2-22-22-2-2-2-22222-22i2i−2i−2i−2i−2i2i2i000000-2200000000−2i−2i2i2i000000000000000000
χ362222-2-2-22-22-2-2-2-22222-2−2i−2i2i2i2i2i−2i−2i000000-22000000002i2i−2i−2i000000000000000000
χ372-2-222-22-2020-22-2002-20i2−i2i2−i2i2−i2i2−i222−2−200002i−2i2i−2i2−200i2−i2i2−i22−2002−2000000000000
χ382-2-222-22-2020-22-2002-20i2−i2i2−i2i2−i2i2−i2−2−2220000−2i2i−2i2i−2200i2−i2i2−i2−2200−22000000000000
χ392-2-222-22-2020-22-2002-20−i2i2−i2i2−i2i2−i2i222−2−20000−2i2i−2i2i2−200−i2i2−i2i22−2002−2000000000000
χ402-2-222-22-2020-22-2002-20−i2i2−i2i2−i2i2−i2i2−2−22200002i−2i2i−2i−2200−i2i2−i2i2−2200−22000000000000
χ412-2-222-22-2020-2-2200-220i2−i2i2−i2i2−i2i2−i222−2−20000−2i2i2i−2i−2200−i2i2−i2i2−22002−2000000000000
χ422-2-222-22-2020-2-2200-220i2−i2i2−i2i2−i2i2−i2−2−22200002i−2i−2i2i2−200−i2i2−i2i22−200−22000000000000
χ432-2-222-22-2020-2-2200-220−i2i2−i2i2−i2i2−i2i222−2−200002i−2i−2i2i−2200i2−i2i2−i2−22002−2000000000000
χ442-2-222-22-2020-2-2200-220−i2i2−i2i2−i2i2−i2i2−2−2220000−2i2i2i−2i2−200i2−i2i2−i22−200−22000000000000
χ452-2-22-22-2-202022-200-2202−2−22−222−222−2−22-2000000−222-22−2−222−200−22000000000000
χ462-2-22-22-2-202022-200-2202−2−22−222−2−2−222-220000002−2-222−2−22−22002−2000000000000
χ472-2-22-22-2-202022-200-220−222−22−2−2222−2−2-22000000−22-22−222−22−200−22000000000000
χ482-2-22-22-2-202022-200-220−222−22−2−22−2−2222-20000002−22-2−222−2−22002−2000000000000
χ492-2-22-22-2-20202-22002-202−2−22−222−222−2−2-220000002−22-2−222−2−2200−22000000000000
χ502-2-22-22-2-20202-22002-202−2−22−222−2−2−2222-2000000−22-22−222−22−2002−2000000000000
χ512-2-22-22-2-20202-22002-20−222−22−2−2222−2−22-20000002−2-222−2−22−2200−22000000000000
χ522-2-22-22-2-20202-22002-20−222−22−2−22−2−222-22000000−222-22−2−222−2002−2000000000000
χ53444444-4-44-44-400-4400-40000000000000000000000000000000000000000000000
χ544444-4-44-4-4-4-4400-440040000000000000000000000000000000000000000000000
χ554-44-4000040-400000000000000002i2−2i22i2−2i20000000000000000002i2−2i20000002-2000000
χ564-44-4000040-400000000000000002i2−2i22i2−2i2000000000000000000−2i22i2000000-22000000
χ574-44-4000040-40000000000000000−2i22i2−2i22i20000000000000000002i2−2i2000000-22000000
χ584-44-4000040-40000000000000000−2i22i2−2i22i2000000000000000000−2i22i20000002-2000000
χ594-4-444-4-440-404000000022−22−222222−22−222200000000000000000000000000000000000000
χ604-4-444-4-440-4040000000−222222−22−222222−2200000000000000000000000000000000000000
χ614-4-44-44440-40-400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ624-4-44-44440-40-40000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ6388-8-8000000000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ6488-8-800000000000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ658-88-80000-808000000000000000000000000000000000000000000000000000000

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