Finite Group Databasebeta

← Group #337739

Character table — Group #337739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888224
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1-1-111-1-1-1-111111111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-11111-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ71111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-11
χ9111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-11111-1-1-1-1-1-11111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-111
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1111111111111-1-1-1-11-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11111-11-1-111-1-1-111
χ17222222222-22-22-22-2-2-22222000000002200-2-2-2-2000000-2-20000000002000000000
χ18222222222-22-22-22-2-2-2222200000000-2-2002222000000-2-2000000000-2000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000000002200-2-22200000022000000000-2000000000
χ20222222222-22-22-22-2-2-2-2-2-2-200000000-2-20022-2-2000000220000000002000000000
χ2122222222-22-22-22-22-2-20000222222-2-200220000-2-200000000000000-20000000000
χ2222222222-22-22-22-22-2-200002222-2-22200-2-20000-2-20000000000000020000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-2222200-2-200002200000000000000-20000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-2-2-2-2-200220000220000000000000020000000000
χ2522-22-22-2-2-202020-200022-2-2i2i2−i2−i2000000002i−2i2i−2ii2−i222−2−2000000i2i2−i2−i20000002−2000
χ2622-22-22-2-2-202020-200022-2-2i2i2−i2−i200000000−2i2i−2i2ii2−i2−2−222000000i2i2−i2−i2000000−22000
χ2722-22-22-2-2-202020-200022-2-2−i2−i2i2i2000000002i−2i2i−2i−i2i2−2−222000000−i2−i2i2i2000000−22000
χ2822-22-22-2-2-202020-200022-2-2−i2−i2i2i200000000−2i2i−2i2i−i2i222−2−2000000−i2−i2i2i20000002−2000
χ2922-22-22-2-2-202020-2000-2-222i2i2−i2−i2000000002i−2i−2i2ii2−i222−2−2000000−i2−i2i2i2000000−22000
χ3022-22-22-2-2-202020-2000-2-222i2i2−i2−i200000000−2i2i2i−2ii2−i2−2−222000000−i2−i2i2i20000002−2000
χ3122-22-22-2-2-202020-2000-2-222−i2−i2i2i2000000002i−2i−2i2i−i2i2−2−222000000i2i2−i2−i20000002−2000
χ3222-22-22-2-2-202020-2000-2-222−i2−i2i2i200000000−2i2i2i−2i−i2i222−2−2000000i2i2−i2−i2000000−22000
χ332-2-222-22-222-2-222-2-22-200000000000000000000002-22-2002i2i−2i−2i0000002i−2i0000000
χ342-2-222-22-222-2-222-2-22-200000000000000000000002-22-200−2i−2i2i2i000000−2i2i0000000
χ352-2-222-22-222-2-222-2-22-20000000000000000000000-22-22002i2i−2i−2i000000−2i2i0000000
χ362-2-222-22-222-2-222-2-22-20000000000000000000000-22-2200−2i−2i2i2i0000002i−2i0000000
χ372-2-2-2-22220-20-20202002−22−22-22-22-200002-200000000002−22−22−22−22−200002−200000
χ382-2-2-2-22220-20-20202002−22−22-22-2-220000-2200000000002−2−22−222−22−20000−2200000
χ392-2-2-2-22220-20-20202002−22−2-22-222-20000-2200000000002−2−22−22−22−2200002−200000
χ402-2-2-2-22220-20-20202002−22−2-22-22-2200002-200000000002−22−22−2−22−220000−2200000
χ412-2-2-2-22220-20-2020200−22−222-22-22-200002-20000000000−22−22−22−22−220000−2200000
χ422-2-2-2-22220-20-2020200−22−222-22-2-220000-220000000000−222−22−2−22−2200002−200000
χ432-2-2-2-22220-20-2020200−22−22-22-222-20000-220000000000−222−22−22−22−20000−2200000
χ442-2-2-2-22220-20-2020200−22−22-22-22-2200002-20000000000−22−22−222−22−200002−200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-44-4040-40-4040000000000004i−4i00000000000000000000000000000000000
χ47444-4-4-44-4040-40-404000000000000−4i4i00000000000000000000000000000000000
χ48444-4-4-44-40-404040-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ49444-4-4-44-40-404040-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ5044-44-44-4-440-40-40400000002i22i2−2i2−2i2000000000000−2i22i20000000000000000000000000
χ5144-44-44-4-440-40-4040000000−2i2−2i22i22i20000000000002i2−2i20000000000000000000000000
χ524-444-4-4-444040-40-40000000000000004i−4i000000000000000000000000000000000
χ534-444-4-4-444040-40-4000000000000000−4i4i000000000000000000000000000000000
χ544-444-4-4-44-40-40404000000000000000000000000022−22−2222000000000000000000000
χ554-444-4-4-44-40-404040000000000000000000000000−222222−22000000000000000000000
χ564-44-444-4-4000000000022−22−22222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ574-44-444-4-4000000000022−22−2222−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ584-44-444-4-40000000000−222222−222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ594-44-444-4-40000000000−222222−22−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ604-4-444-44-44-4-444-4-44-4400000000000000000000000000000000000000000000000
χ614-4-444-44-4-444-4-444-4-4400000000000000000000000000000000000000000000000
χ624-4-444-44-4-4-444-4-4444-400000000000000000000000000000000000000000000000
χ634-4-4-4-444404040-40-40022−2222−220000000000000000000000−22220000000000000000000
χ644-4-4-4-444404040-40-400−2222−2222000000000000000000000022−220000000000000000000
χ6588-8-88-8-88000000000000000000000000000000000000000000000000000000000

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