Finite Group Databasebeta

← Group #284905

Character table — Group #284905

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222244444444444444444448888888888888888888888161616161616161616323232
order12222244444444444448888888888882224448888888888888888444444888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-1111-1-1-1
χ4111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ61111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
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
χ111111111111111-1-11-1-1111111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11-1-11-11
χ121111111111111-1-11-1-1111111111-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-111-11-1
χ131111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111-1-11111-1-111-1-111111-1-11-1-1
χ141111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-111
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
χ172222222-222-22-222-222-2000000000000-222-2-2-2-2-200002200000000000000000000
χ182222222-222-22-222-222-2000000000000-2-2-222-2220000-2-200000000000000000000
χ192222222-222-22-2-2-2-2-2-2-2000000000000222-2-22220000-2-200000000000000000000
χ202222222-222-22-2-2-2-2-2-2-20000000000002-2-2222-2-200002200000000000000000000
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
χ252222-2-222-222-2-222-2-2-22000000002222-200002002200000000-2-2-2-2000000000000
χ262222-2-222-222-2-222-2-2-2200000000-2-2-2-2-20000200-2-2000000002222000000000000
χ272222-2-222-222-2-2-2-2-222200000000222220000-200-2-20000000022-2-2000000000000
χ282222-2-222-222-2-2-2-2-222200000000-2-2-2-220000-2002200000000-2-222000000000000
χ292222-2-22-2-22-2-22222-2-2-22i2i−2i−2i−2i−2i2i2i000020000-2000000002i2i−2i−2i0000000000000000
χ302222-2-22-2-22-2-22222-2-2-2−2i−2i2i2i2i2i−2i−2i000020000-200000000−2i−2i2i2i0000000000000000
χ312222-2-22-2-22-2-22-2-2222-22i2i−2i−2i−2i−2i2i2i0000-20000200000000−2i−2i2i2i0000000000000000
χ322222-2-22-2-22-2-22-2-2222-2−2i−2i2i2i2i2i−2i−2i0000-200002000000002i2i−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
χ372-2-222-220-2-20202i−2i02i−2i02−22−22−22−222−2−20002i−2i02-2i2−i20000i2−i2i2−i2i2−i22−2000000000000
χ382-2-222-220-2-20202i−2i02i−2i02−22−22−22−2−2−222000−2i2i0-22−i2i20000i2−i2i2−i2−i2i2−22000000000000
χ392-2-222-220-2-20202i−2i02i−2i0−22−22−22−2222−2−2000−2i2i0-22i2−i20000−i2i2−i2i2i2−i22−2000000000000
χ402-2-222-220-2-20202i−2i02i−2i0−22−22−22−22−2−2220002i−2i02-2−i2i20000−i2i2−i2i2−i2i2−22000000000000
χ412-2-222-220-2-2020−2i2i0−2i2i02−22−22−22−222−2−2000−2i2i02-2−i2i20000−i2i2−i2i2−i2i22−2000000000000
χ422-2-222-220-2-2020−2i2i0−2i2i02−22−22−22−2−2−2220002i−2i0-22i2−i20000−i2i2−i2i2i2−i2−22000000000000
χ432-2-222-220-2-2020−2i2i0−2i2i0−22−22−22−2222−2−20002i−2i0-22−i2i20000i2−i2i2−i2−i2i22−2000000000000
χ442-2-222-220-2-2020−2i2i0−2i2i0−22−22−22−22−2−222000−2i2i02-2i2−i20000i2−i2i2−i2i2−i2−22000000000000
χ452-2-22-22202-20-202i−2i0−2i2i0i2−i2−i2i2−i2i2i2−i222−2−202-200000i2−i2002i−2i−222−2−i2i2−22000000000000
χ462-2-22-22202-20-202i−2i0−2i2i0i2−i2−i2i2−i2i2i2−i2−2−2220-2200000−i2i200−2i2i−222−2i2−i22−2000000000000
χ472-2-22-22202-20-202i−2i0−2i2i0−i2i2i2−i2i2−i2−i2i222−2−20-2200000i2−i200−2i2i2−2−22−i2i2−22000000000000
χ482-2-22-22202-20-202i−2i0−2i2i0−i2i2i2−i2i2−i2−i2i2−2−22202-200000−i2i2002i−2i2−2−22i2−i22−2000000000000
χ492-2-22-22202-20-20−2i2i02i−2i0i2−i2−i2i2−i2i2i2−i222−2−20-2200000−i2i2002i−2i2−2−22i2−i2−22000000000000
χ502-2-22-22202-20-20−2i2i02i−2i0i2−i2−i2i2−i2i2i2−i2−2−22202-200000i2−i200−2i2i2−2−22−i2i22−2000000000000
χ512-2-22-22202-20-20−2i2i02i−2i0−i2i2i2−i2i2−i2−i2i222−2−202-200000−i2i200−2i2i−222−2i2−i2−22000000000000
χ522-2-22-22202-20-20−2i2i02i−2i0−i2i2i2−i2i2−i2−i2i2−2−2220-2200000i2−i2002i−2i−222−2−i2i22−2000000000000
χ53444444-44-4-44-4-400400-40000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-44-40040040000000000000000000000000000000000000000000000
χ554-44-4000-4004000000000000000022−2222−2200000000002i2−2i2000000000000002i−2i000000
χ564-44-4000-4004000000000000000022−2222−220000000000−2i22i200000000000000−2i2i000000
χ574-44-4000-40040000000000000000−2222−222200000000002i2−2i200000000000000−2i2i000000
χ584-44-4000-40040000000000000000−2222−22220000000000−2i22i2000000000000002i−2i000000
χ594-4-444-4-40440-400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ604-4-444-4-40440-40000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ614-4-44-44-40-4404000000022−2222−22−2222−222200000000000000000000000000000000000000
χ624-4-44-44-40-44040000000−2222−222222−2222−2200000000000000000000000000000000000000
χ6388-8-8000000000000000000000004-4-440000000000000000000000000000000000
χ6488-8-800000000000000000000000-444-40000000000000000000000000000000000
χ658-88-8000800-8000000000000000000000000000000000000000000000000000000

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