Finite Group Databasebeta

← Group #335753

Character table — Group #335753

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888824448888244
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-11-1-111-1-1-1
χ311111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1111111111-1-1-111-1-1-1-1-1
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
χ61111111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-111-1-1-111-1-11
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
χ9111111111111111111-1-1-1-111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-111-111-1-11-1-1
χ11111111111111111111-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111111-111
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-11-1
χ172222222222-2-2-222-2-2-20000222200220000-2-2-2-200-2-200000000000020000000000
χ182222222222-2-2-222-2-2-20000222200-2-20000222200-2-2000000000000-20000000000
χ192222222222-2-2-222-2-2-20000-2-2-2-200220000-2-2220022000000000000-20000000000
χ202222222222-2-2-222-2-2-20000-2-2-2-200-2-2000022-2-2002200000000000020000000000
χ2122222222-2-2222-2-22-2-2222200002200-2-2-2-20000-2-20000000000000000020000000
χ2222222222-2-2222-2-22-2-222220000-2-20022220000-2-200000000000000000-20000000
χ2322222222-2-2222-2-22-2-2-2-2-2-20000220022-2-200002200000000000000000-20000000
χ2422222222-2-2222-2-22-2-2-2-2-2-20000-2-200-2-2220000220000000000000000020000000
χ2522-2-222-2-22-20002-2000i2i2−i2−i222-2-2000000002i−2i2i−2ii2−i200000022−2−2i2i2−i2−i200002−200000
χ2622-2-222-2-22-20002-2000i2i2−i2−i222-2-200000000−2i2i−2i2ii2−i2000000−2−222i2i2−i2−i20000−2200000
χ2722-2-222-2-22-20002-2000i2i2−i2−i2-2-222000000002i−2i−2i2ii2−i200000022−2−2−i2−i2i2i20000−2200000
χ2822-2-222-2-22-20002-2000i2i2−i2−i2-2-22200000000−2i2i2i−2ii2−i2000000−2−222−i2−i2i2i200002−200000
χ2922-2-222-2-22-20002-2000−i2−i2i2i222-2-2000000002i−2i2i−2i−i2i2000000−2−222−i2−i2i2i20000−2200000
χ3022-2-222-2-22-20002-2000−i2−i2i2i222-2-200000000−2i2i−2i2i−i2i200000022−2−2−i2−i2i2i200002−200000
χ3122-2-222-2-22-20002-2000−i2−i2i2i2-2-222000000002i−2i−2i2i−i2i2000000−2−222i2i2−i2−i200002−200000
χ3222-2-222-2-22-20002-2000−i2−i2i2i2-2-22200000000−2i2i2i−2i−i2i200000022−2−2i2i2−i2−i20000−2200000
χ332-22-22-22-222-22-2-2-22-220000000000000000000000002i2i−2i−2i2-22-2000002i−2i00000000
χ342-22-22-22-222-22-2-2-22-220000000000000000000000002i2i−2i−2i-22-2200000−2i2i00000000
χ352-22-22-22-222-22-2-2-22-22000000000000000000000000−2i−2i2i2i2-22-200000−2i2i00000000
χ362-22-22-22-222-22-2-2-22-22000000000000000000000000−2i−2i2i2i-22-22000002i−2i00000000
χ372-2-22-222-20022-200-2002i−2i2i−2i2−22−200002-22i−2i0000002−2i2−i2i2−i20000i2−i2i2−i20000002−2000
χ382-2-22-222-20022-200-2002i−2i2i−2i2−22−20000-22−2i2i0000002−2−i2i2−i2i20000i2−i2i2−i2000000−22000
χ392-2-22-222-20022-200-2002i−2i2i−2i−22−2200002-22i−2i000000−22−i2i2−i2i20000−i2i2−i2i2000000−22000
χ402-2-22-222-20022-200-2002i−2i2i−2i−22−220000-22−2i2i000000−22i2−i2i2−i20000−i2i2−i2i20000002−2000
χ412-2-22-222-20022-200-200−2i2i−2i2i2−22−200002-2−2i2i0000002−2−i2i2−i2i20000−i2i2−i2i20000002−2000
χ422-2-22-222-20022-200-200−2i2i−2i2i2−22−20000-222i−2i0000002−2i2−i2i2−i20000−i2i2−i2i2000000−22000
χ432-2-22-222-20022-200-200−2i2i−2i2i−22−2200002-2−2i2i000000−22i2−i2i2−i20000i2−i2i2−i2000000−22000
χ442-2-22-222-20022-200-200−2i2i−2i2i−22−220000-222i−2i000000−22−i2i2−i2i20000i2−i2i2−i20000002−2000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ4644-4-444-4-4-44000-440002i22i2−2i2−2i20000000000000000−2i22i20000000000000000000000000
χ4744-4-444-4-4-44000-44000−2i2−2i22i22i200000000000000002i2−2i20000000000000000000000000
χ4844-4-4-4-444004-4-400400000000004-40000000000000000000000000000000000000
χ4944-4-4-4-444004-4-40040000000000-440000000000000000000000000000000000000
χ5044-4-4-4-44400-44400-40000000000000000000000000022−22−22220000000000000000000
χ5144-4-4-4-44400-44400-400000000000000000000000000−222222−220000000000000000000
χ524-44-44-44-4444-44-4-4-44-400000000000000000000000000000000000000000000000
χ534-44-44-44-4-4-44-4444-4-4400000000000000000000000000000000000000000000000
χ544-44-44-44-4-4-4-44-44444-400000000000000000000000000000000000000000000000
χ554-44-4-44-44000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ564-44-4-44-44000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ574-44-4-44-440000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ584-44-4-44-440000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ594-4-444-4-444-4000-44000000000000000000000000000000022−22−2222000000000000000
χ604-4-444-4-444-4000-440000000000000000000000000000000−222222−22000000000000000
χ614-4-444-4-44-440004-400000000000004-400000000000000000000000000000000000
χ624-4-444-4-44-440004-40000000000000-4400000000000000000000000000000000000
χ634-4-44-444-400-4-4400400000022−2222−2200000000000000−222200000000000000000000000
χ644-4-44-444-400-4-44004000000−2222−22220000000000000022−2200000000000000000000000
χ658888-8-8-8-8000000000000000000000000000000000000000000000000000000000

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