Finite Group Databasebeta

← Group #284909

Character table — Group #284909

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222244444444444444444448888888888888888888888161616161616161616323232
order12222244444444444448888888888882444448888888888888888244444888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111-1-1-1
χ4111111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ61111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ91111111111111-1-11-1-11111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1111-1-1-11-1
χ101111111111111-1-11-1-11111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1111-11
χ111111111111111-1-11-1-1111111111-1-1-1-1-111-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11-1-11-11
χ121111111111111-1-11-1-1111111111-1-1-1-1-111-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-111-11-1
χ131111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-111-111-1-1-1-111-1-11111-1-111-1-111111-1-11-1-1
χ141111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-111-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-111
χ151111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-11-1-1-111
χ161111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-111-1-111-1111-1-1
χ1722222222-222-2-222-222-2000000000000-222-2-2-2-2-200002200000000000000000000
χ1822222222-222-2-222-222-2000000000000-2-2-2-222220000-2-200000000000000000000
χ1922222222-222-2-2-2-2-2-2-2-20000000000002222-2-2220000-2-200000000000000000000
χ2022222222-222-2-2-2-2-2-2-2-20000000000002-2-2222-2-200002200000000000000000000
χ21222222-2-2-2-2-2-2200-20022i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-20002i−2i000
χ22222222-2-2-2-2-2-2200-20022i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22000−2i2i000
χ23222222-2-2-2-2-2-2200-2002−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-2000−2i2i000
χ24222222-2-2-2-2-2-2200-2002−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-220002i−2i000
χ252222-2-22-222-22-222-2-2-22000000002222-20020000-2-20000000022-2-2000000000000
χ262222-2-22-222-22-222-2-2-2200000000-2-2-2-2-200200002200000000-2-222000000000000
χ272222-2-22-222-22-2-2-2-2222000000002222200-200002200000000-2-2-2-2000000000000
χ282222-2-22-222-22-2-2-2-222200000000-2-2-2-2200-20000-2-2000000002222000000000000
χ292222-2-22-2-22-2-22222-2-2-22i2i−2i−2i−2i−2i2i2i0000200-200000000002i2i−2i−2i0000000000000000
χ302222-2-22-2-22-2-22222-2-2-2−2i−2i2i2i2i2i−2i−2i0000200-20000000000−2i−2i2i2i0000000000000000
χ312222-2-22-2-22-2-22-2-2222-22i2i−2i−2i−2i−2i2i2i0000-20020000000000−2i−2i2i2i0000000000000000
χ322222-2-22-2-22-2-22-2-2222-2−2i−2i2i2i2i2i−2i−2i0000-200200000000002i2i−2i−2i0000000000000000
χ332222-2-2-222-222200-200-22222-2-2-2-200000000000000220000000000-220000-200000
χ342222-2-2-222-222200-200-22222-2-2-2-200000000000000-2-200000000002-20000200000
χ352222-2-2-222-222200-200-2-2-2-2-22222000000000000002200000000002-20000-200000
χ362222-2-2-222-222200-200-2-2-2-2-2222200000000000000-2-20000000000-220000200000
χ372-22-22-2-2-2022002i−2i02i−2i0i2−i2i2−i2i2−i2i2−i222−2−200002-22i−2ii2−i200002−22−2i2−i22−2000000000000
χ382-22-22-2-2-2022002i−2i02i−2i0i2−i2i2−i2i2−i2i2−i2−2−2220000-22−2i2i−i2i200002−22−2−i2i2−22000000000000
χ392-22-22-2-2-2022002i−2i02i−2i0−i2i2−i2i2−i2i2−i2i222−2−20000-22−2i2ii2−i20000−22−22i2−i22−2000000000000
χ402-22-22-2-2-2022002i−2i02i−2i0−i2i2−i2i2−i2i2−i2i2−2−22200002-22i−2i−i2i20000−22−22−i2i2−22000000000000
χ412-22-22-2-2-202200−2i2i0−2i2i0i2−i2i2−i2i2−i2i2−i222−2−20000-222i−2i−i2i20000−22−22−i2i22−2000000000000
χ422-22-22-2-2-202200−2i2i0−2i2i0i2−i2i2−i2i2−i2i2−i2−2−22200002-2−2i2ii2−i20000−22−22i2−i2−22000000000000
χ432-22-22-2-2-202200−2i2i0−2i2i0−i2i2−i2i2−i2i2−i2i222−2−200002-2−2i2i−i2i200002−22−2−i2i22−2000000000000
χ442-22-22-2-2-202200−2i2i0−2i2i0−i2i2−i2i2−i2i2−i2i2−2−2220000-222i−2ii2−i200002−22−2i2−i2−22000000000000
χ452-22-2-22-2202-2002i−2i0−2i2i02−2−22−222−222−2−202i−2i00000−i2i2002-2−i2i2i2−i2i2−i2−22000000000000
χ462-22-2-22-2202-2002i−2i0−2i2i02−2−22−222−2−2−2220−2i2i00000i2−i200-22−i2i2i2−i2−i2i22−2000000000000
χ472-22-2-22-2202-2002i−2i0−2i2i0−222−22−2−2222−2−20−2i2i00000−i2i200-22i2−i2−i2i2i2−i2−22000000000000
χ482-22-2-22-2202-2002i−2i0−2i2i0−222−22−2−22−2−22202i−2i00000i2−i2002-2i2−i2−i2i2−i2i22−2000000000000
χ492-22-2-22-2202-200−2i2i02i−2i02−2−22−222−222−2−20−2i2i00000i2−i2002-2i2−i2−i2i2−i2i2−22000000000000
χ502-22-2-22-2202-200−2i2i02i−2i02−2−22−222−2−2−22202i−2i00000−i2i200-22i2−i2−i2i2i2−i22−2000000000000
χ512-22-2-22-2202-200−2i2i02i−2i0−222−22−2−2222−2−202i−2i00000i2−i200-22−i2i2i2−i2−i2i2−22000000000000
χ522-22-2-22-2202-200−2i2i02i−2i0−222−22−2−22−2−2220−2i2i00000−i2i2002-2−i2i2i2−i2i2−i22−2000000000000
χ53444444-4-44-4-44-400400-40000000000000000000000000000000000000000000000
χ544444-4-4-44-4-44-4-40040040000000000000000000000000000000000000000000000
χ554-44-44-4440-4-40000000022−22−222222−22−222200000000000000000000000000000000000000
χ564-44-44-4440-4-400000000−222222−22−222222−2200000000000000000000000000000000000000
χ574-44-4-444-40-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ584-44-4-444-40-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ594-4-440000400-400000000000000022−2222−2200000000002i2−2i2000000000000002i−2i000000
χ604-4-440000400-400000000000000022−2222−220000000000−2i22i200000000000000−2i2i000000
χ614-4-440000400-4000000000000000−2222−222200000000002i2−2i200000000000000−2i2i000000
χ624-4-440000400-4000000000000000−2222−22220000000000−2i22i2000000000000002i−2i000000
χ6388-8-8000000000000000000000004-4-440000000000000000000000000000000000
χ6488-8-800000000000000000000000-444-40000000000000000000000000000000000
χ658-8-880000-800800000000000000000000000000000000000000000000000000000

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