Finite Group Databasebeta

← Group #326113

Character table — Group #326113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888822444444444488888888888888888824884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ711111111111111111111111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-11-1
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111111111-1-111-1-1
χ17222222222-22-22-22-2-2-200000000222222002200-2-2-2-2-2-2000000000000000000000000
χ18222222222-22-22-22-2-2-2000000002222-2-200-2-2002222-2-2000000000000000000000000
χ19222222222-22-22-22-2-2-200000000-2-2-2-22200-2-200-2-22222000000000000000000000000
χ20222222222-22-22-22-2-2-200000000-2-2-2-2-2-200220022-2-222000000000000000000000000
χ2122222222-22-22-22-22-2-22222-2-2-2-20000002200-2-200000000000000000000002-2000000
χ2222222222-22-22-22-22-2-22222-2-2-2-2000000-2-200220000000000000000000000-22000000
χ2322222222-22-22-22-22-2-2-2-2-2-222220000002200-2-20000000000000000000000-22000000
χ2422222222-22-22-22-22-2-2-2-2-2-22222000000-2-2002200000000000000000000002-2000000
χ2522-22-2-2-22-202020-2000i2i2−i2−i2i2i2−i2−i22i2i−2i−2i2-2002i−2i0000000022−2−20000i2i2−i2−i222−2−200000000
χ2622-22-2-2-22-202020-2000i2i2−i2−i2i2i2−i2−i22i2i−2i−2i-2200−2i2i00000000−2−2220000−i2−i2i2i222−2−200000000
χ2722-22-2-2-22-202020-2000i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i2-200−2i2i00000000−2−2220000i2i2−i2−i2−2−22200000000
χ2822-22-2-2-22-202020-2000i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i-22002i−2i0000000022−2−20000−i2−i2i2i2−2−22200000000
χ2922-22-2-2-22-202020-2000−i2−i2i2i2−i2−i2i2i22i2i−2i−2i2-2002i−2i00000000−2−2220000−i2−i2i2i2−2−22200000000
χ3022-22-2-2-22-202020-2000−i2−i2i2i2−i2−i2i2i22i2i−2i−2i-2200−2i2i0000000022−2−20000i2i2−i2−i2−2−22200000000
χ3122-22-2-2-22-202020-2000−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i2-200−2i2i0000000022−2−20000−i2−i2i2i222−2−200000000
χ3222-22-2-2-22-202020-2000−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i-22002i−2i00000000−2−2220000i2i2−i2−i222−2−200000000
χ332-2222-2-2-2-20-202020002−22−22−22−22-22-2000000002i−2i2i−2i00i2−i2i2−i20000i2−i2i2−i22−22−200000000
χ342-2222-2-2-2-20-202020002−22−22−22−22-22-200000000−2i2i−2i2i00−i2i2−i2i20000−i2i2−i2i22−22−200000000
χ352-2222-2-2-2-20-202020002−22−22−22−2-22-22000000002i−2i−2i2i00−i2i2−i2i20000i2−i2i2−i2−22−2200000000
χ362-2222-2-2-2-20-202020002−22−22−22−2-22-2200000000−2i2i2i−2i00i2−i2i2−i20000−i2i2−i2i2−22−2200000000
χ372-2222-2-2-2-20-20202000−22−22−22−222-22-2000000002i−2i2i−2i00−i2i2−i2i20000−i2i2−i2i2−22−2200000000
χ382-2222-2-2-2-20-20202000−22−22−22−222-22-200000000−2i2i−2i2i00i2−i2i2−i20000i2−i2i2−i2−22−2200000000
χ392-2222-2-2-2-20-20202000−22−22−22−22-22-22000000002i−2i−2i2i00i2−i2i2−i20000−i2i2−i2i22−22−200000000
χ402-2222-2-2-2-20-20202000−22−22−22−22-22-2200000000−2i2i2i−2i00−i2i2−i2i20000i2−i2i2−i22−22−200000000
χ412-2-22-222-222-2-222-2-2-222i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000002i−2i0000000000002-2-2200000000
χ422-2-22-222-222-2-222-2-2-222i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000−2i2i000000000000-222-200000000
χ432-2-22-222-222-2-222-2-2-22−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000002i−2i000000000000-222-200000000
χ442-2-22-222-222-2-222-2-2-22−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000−2i2i0000000000002-2-2200000000
χ452-2-22-222-22-2-222-2-222-2000000002i−2i−2i2i000000000000−2i2i2i−2i−2i2i0000-222-2000000000000
χ462-2-22-222-22-2-222-2-222-2000000002i−2i−2i2i000000000000−2i2i−2i2i2i−2i00002-2-22000000000000
χ472-2-22-222-22-2-222-2-222-200000000−2i2i2i−2i0000000000002i−2i2i−2i−2i2i00002-2-22000000000000
χ482-2-22-222-22-2-222-2-222-200000000−2i2i2i−2i0000000000002i−2i−2i2i2i−2i0000-222-2000000000000
χ492-2-22-222-2-222-2-222-22-22i−2i−2i2i−2i2i2i−2i00000000000000000000002i2i−2i−2i00000000002-20000
χ502-2-22-222-2-222-2-222-22-22i−2i−2i2i−2i2i2i−2i0000000000000000000000−2i−2i2i2i0000000000-220000
χ512-2-22-222-2-222-2-222-22-2−2i2i2i−2i2i−2i−2i2i00000000000000000000002i2i−2i−2i0000000000-220000
χ522-2-22-222-2-222-2-222-22-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000−2i−2i2i2i00000000002-20000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ54444-4-4-44-404040-40-400000000000000004-40000000000000000000000000000000000
χ55444-4-4-44-404040-40-40000000000000000-440000000000000000000000000000000000
χ56444-4-4-44-40-40-40404000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ57444-4-4-44-40-40-4040400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ5844-44-4-4-4440-40-4040002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5944-44-4-4-4440-40-404000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ604-4444-4-4-44040-40-400022−2222−22−2222−2222000000000000000000000000000000000000000000
χ614-4444-4-4-44040-40-4000−2222−222222−2222−22000000000000000000000000000000000000000000
χ624-4-44-444-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ634-4-4-44-444040-40-404000000000000000000004-4000000000000000000000000000000
χ644-4-4-44-444040-40-40400000000000000000000-44000000000000000000000000000000
χ654-4-4-44-4440-404040-40000000000000000000000000000000022−22−22220000000000000000
χ664-4-4-44-4440-404040-400000000000000000000000000000000−222222−220000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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