Finite Group Databasebeta

← Group #331730

Character table — Group #331730

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888822248888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-111-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-11111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1111-1-1
χ11111111111111111111-1-1-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111111-111
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-11-1-1111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-11-1
χ17222222222-22-22-22-2-2-20000222200220000-2-2-2-200-2-200000000000020000000000
χ18222222222-22-22-22-2-2-20000222200-2-20000222200-2-2000000000000-20000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200220000-2-2220022000000000000-20000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-200-2-2000022-2-2002200000000000020000000000
χ2122222222-22-22-22-22-2-2222200002200-2-2-2-20000-2-20000000000000000020000000
χ2222222222-22-22-22-22-2-222220000-2-20022220000-2-200000000000000000-20000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002200-2-22200002200000000000000000-20000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000-2-20022-2-20000220000000000000000020000000
χ2522-22-22-2-220-20-202000i2i2−i2−i222-2-2000000002i−2i2i−2ii2−i200000022−2−2i2i2−i2−i20000002−2000
χ2622-22-22-2-220-20-202000i2i2−i2−i222-2-200000000−2i2i−2i2ii2−i2000000−2−222i2i2−i2−i2000000−22000
χ2722-22-22-2-220-20-202000i2i2−i2−i2-2-222000000002i−2i−2i2ii2−i200000022−2−2−i2−i2i2i2000000−22000
χ2822-22-22-2-220-20-202000i2i2−i2−i2-2-22200000000−2i2i2i−2ii2−i2000000−2−222−i2−i2i2i20000002−2000
χ2922-22-22-2-220-20-202000−i2−i2i2i222-2-2000000002i−2i2i−2i−i2i2000000−2−222−i2−i2i2i2000000−22000
χ3022-22-22-2-220-20-202000−i2−i2i2i222-2-200000000−2i2i−2i2i−i2i200000022−2−2−i2−i2i2i20000002−2000
χ3122-22-22-2-220-20-202000−i2−i2i2i2-2-222000000002i−2i−2i2i−i2i2000000−2−222i2i2−i2−i20000002−2000
χ3222-22-22-2-220-20-202000−i2−i2i2i2-2-22200000000−2i2i2i−2i−i2i200000022−2−2i2i2−i2−i2000000−22000
χ332-22-2-222-202020-20-2002i−2i2i−2i2−22−200002i−2i2-20000002−2i2i2−i2−i20000i2−i2i2−i200002−200000
χ342-22-2-222-202020-20-2002i−2i2i−2i2−22−20000−2i2i-220000002−2−i2−i2i2i20000i2−i2i2−i20000−2200000
χ352-22-2-222-202020-20-2002i−2i2i−2i−22−2200002i−2i2-2000000−22−i2−i2i2i20000−i2i2−i2i20000−2200000
χ362-22-2-222-202020-20-2002i−2i2i−2i−22−220000−2i2i-22000000−22i2i2−i2−i20000−i2i2−i2i200002−200000
χ372-22-2-222-202020-20-200−2i2i−2i2i2−22−200002i−2i-220000002−2i2i2−i2−i20000−i2i2−i2i20000−2200000
χ382-22-2-222-202020-20-200−2i2i−2i2i2−22−20000−2i2i2-20000002−2−i2−i2i2i20000−i2i2−i2i200002−200000
χ392-22-2-222-202020-20-200−2i2i−2i2i−22−2200002i−2i-22000000−22−i2−i2i2i20000i2−i2i2−i200002−200000
χ402-22-2-222-202020-20-200−2i2i−2i2i−22−220000−2i2i2-2000000−22i2i2−i2−i20000i2−i2i2−i20000−2200000
χ412-2-222-22-222-2-222-2-22-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000002-200000000
χ422-2-222-22-222-2-222-2-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i00000-2200000000
χ432-2-222-22-222-2-222-2-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000-2200000000
χ442-2-222-22-222-2-222-2-22-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000002-200000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ4644-44-44-4-4-404040-40002i22i2−2i2−2i20000000000000000−2i22i20000000000000000000000000
χ4744-44-44-4-4-404040-4000−2i2−2i22i22i200000000000000002i2−2i20000000000000000000000000
χ4844-4-4-4-444040-40-4040000000000000000000000000022−22−22220000000000000000000
χ4944-4-4-4-444040-40-40400000000000000000000000000−222222−220000000000000000000
χ5044-4-4-4-4440-404040-400000000004-40000000000000000000000000000000000000
χ5144-4-4-4-4440-404040-40000000000-440000000000000000000000000000000000000
χ524-444-4-4-444040-40-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ534-444-4-4-444040-40-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ544-444-4-4-44-40-4040400000000000004-400000000000000000000000000000000000
χ554-444-4-4-44-40-404040000000000000-4400000000000000000000000000000000000
χ564-44-4-444-40-40-4040400000022−2222−2200000000000000−222200000000000000000000000
χ574-44-4-444-40-40-40404000000−2222−22220000000000000022−2200000000000000000000000
χ584-4-444-44-44-4-444-4-44-4400000000000000000000000000000000000000000000000
χ594-4-444-44-4-444-4-444-4-4400000000000000000000000000000000000000000000000
χ604-4-444-44-4-4-444-4-4444-400000000000000000000000000000000000000000000000
χ614-4-4-444-44000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ624-4-4-444-44000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ634-4-4-444-440000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ644-4-4-444-440000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ65888-88-8-8-8000000000000000000000000000000000000000000000000000000000

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