Finite Group Databasebeta

← Group #300075

Character table — Group #300075

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244444444224444888888884444448888888888888888222244444488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-11-11-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-11
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-11-1-1-1-11-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11-11111-11-1
χ911111111111111-1-11-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-111-1-1
χ1011111111111111-1-11-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11-1-111
χ1111111111111111-1-11-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-111
χ1211111111111111-1-11-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1
χ1311111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-11-1-1-111-1-11
χ1411111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11-1111-1-111-1
χ1511111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-11-1-1-11-111-1
χ1611111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11-1111-11-1-11
χ172222222-2-222-2-2222-222-200000000-2-222-2-222-2-2000000000000000000000000
χ182222222-2-222-2-2222-222-200000000-2-2-2-222-2-222000000000000000000000000
χ192222222-2-222-2-22-2-2-2-2-2-2000000002222-2-2-2-222000000000000000000000000
χ202222222-2-222-2-22-2-2-2-2-2-20000000022-2-22222-2-2000000000000000000000000
χ21222222-2-2-2-2-222-200-20022222-2-2-2-200000000000000000000002-20002-200000
χ22222222-2-2-2-2-222-200-20022222-2-2-2-20000000000000000000000-22000-2200000
χ23222222-2-2-2-2-222-200-2002-2-2-2-2222200000000000000000000002-2000-2200000
χ24222222-2-2-2-2-222-200-2002-2-2-2-222220000000000000000000000-220002-200000
χ252222-2-2222-2-2-2-2222-2-2-22000000002-20000000022-2-2000022-2-2000000000000
χ262222-2-2222-2-2-2-2222-2-2-22000000002-200000000-2-2220000-2-222000000000000
χ272222-2-2222-2-2-2-22-2-2-222200000000-220000000022-2-20000-2-222000000000000
χ282222-2-2222-2-2-2-22-2-2-222200000000-2200000000-2-222000022-2-2000000000000
χ292222-2-22-2-2-2-2222222-2-2-222-2-222-2-2-2200000000000022-2-20000000000000000
χ302222-2-22-2-2-2-2222222-2-2-2-2-222-2-222-22000000000000-2-2220000000000000000
χ312222-2-22-2-2-2-2222-2-2222-222-2-222-2-22-2000000000000-2-2220000000000000000
χ322222-2-22-2-2-2-2222-2-2222-2-2-222-2-2222-200000000000022-2-20000000000000000
χ332222-2-2-2222222-200-200-222-2-2-2-22200000000000000000000000022-200-20000
χ342222-2-2-2222222-200-200-222-2-2-2-222000000000000000000000000-2-220020000
χ352222-2-2-2222222-200-200-2-2-22222-2-20000000000000000000000002-2-20020000
χ362222-2-2-2222222-200-200-2-2-22222-2-2000000000000000000000000-22200-20000
χ372-22-22-22002-200-22-202-202−22−22−22−200002i−2i002i−2ii2−i2i2−i22−22−2i2−i2i2−i2000000000000
χ382-22-22-22002-200-22-202-202−22−22−22−20000−2i2i00−2i2i−i2i2−i2i22−22−2−i2i2−i2i2000000000000
χ392-22-22-22002-200-22-202-20−22−22−22−2200002i−2i002i−2i−i2i2−i2i2−22−22−i2i2−i2i2000000000000
χ402-22-22-22002-200-22-202-20−22−22−22−220000−2i2i00−2i2ii2−i2i2−i2−22−22i2−i2i2−i2000000000000
χ412-22-22-22002-200-2-220-2202−22−22−22−200002i−2i00−2i2i−i2i2−i2i2−22−22i2−i2i2−i2000000000000
χ422-22-22-22002-200-2-220-2202−22−22−22−20000−2i2i002i−2ii2−i2i2−i2−22−22−i2i2−i2i2000000000000
χ432-22-22-22002-200-2-220-220−22−22−22−2200002i−2i00−2i2ii2−i2i2−i22−22−2−i2i2−i2i2000000000000
χ442-22-22-22002-200-2-220-220−22−22−22−220000−2i2i002i−2i−i2i2−i2i22−22−2i2−i2i2−i2000000000000
χ452-22-2-22200-2200-22-20-2202−2−222−2−22002i−2i002i−2i00i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ462-22-2-22200-2200-22-20-2202−2−222−2−2200−2i2i00−2i2i00−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ472-22-2-22200-2200-22-20-220−222−2−222−2002i−2i002i−2i00−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ482-22-2-22200-2200-22-20-220−222−2−222−200−2i2i00−2i2i00i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ492-22-2-22200-2200-2-2202-202−2−222−2−22002i−2i00−2i2i00−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ502-22-2-22200-2200-2-2202-202−2−222−2−2200−2i2i002i−2i00i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ512-22-2-22200-2200-2-2202-20−222−2−222−2002i−2i00−2i2i00i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ522-22-2-22200-2200-2-2202-20−222−2−222−200−2i2i002i−2i00−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ53444444-444-4-4-4-4-400400-4000000000000000000000000000000000000000000
χ544444-4-4-4-4-444-4-4-4004004000000000000000000000000000000000000000000
χ554-44-44-4-400-4400400000022−2222−22−2222−22220000000000000000000000000000000000
χ564-44-44-4-400-44004000000−2222−222222−2222−220000000000000000000000000000000000
χ574-44-4-44-4004-400400000022−22−2222−222222−220000000000000000000000000000000000
χ584-44-4-44-4004-4004000000−222222−2222−22−22220000000000000000000000000000000000
χ5988-8-80008-800000000000000000000000000000000000000000000000000000
χ6088-8-8000-8800000000000000000000000000000000000000000000000000000
χ618-8-8800000008-80000000000000000000000000000000000000000000000000
χ628-8-880000000-880000000000000000000000000000000000000000000000000

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