Finite Group Databasebeta

← Group #337671

Character table — Group #337671

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888844448888244
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-111111-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-11111-1-11-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-11111-111
χ9111111111111111111-1-1-1-1111111-1-111111111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-11
χ11111111111111111111-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-11-1
χ17222222222-22-22-22-2-2-20000222200002200-2-22200-2-2000000000000-20000000000
χ18222222222-22-22-22-2-2-2000022220000-2-20022-2-200-2-200000000000020000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200002200-2-2-2-2002200000000000020000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-20000-2-20022220022000000000000-20000000000
χ2122222222-22-22-22-22-2-222220000222200-2-20000-2-2000000000000000-2000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-200220000-2-20000000000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000022-2-200-2-20000220000000000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000-2-2220022000022000000000000000-2000000000
χ2522-2-2-222-22020-20-200022−2−22i2i−2i−2i00002i−2i00002-22−200i2i2−i2−i20000i2i2−i2−i20000002−2000
χ2622-2-2-222-22020-20-200022−2−22i2i−2i−2i0000−2i2i0000-222−200−i2−i2i2i20000i2i2−i2−i2000000−22000
χ2722-2-2-222-22020-20-200022−2−2−2i−2i2i2i00002i−2i0000-222−200i2i2−i2−i20000−i2−i2i2i2000000−22000
χ2822-2-2-222-22020-20-200022−2−2−2i−2i2i2i0000−2i2i00002-22−200−i2−i2i2i20000−i2−i2i2i20000002−2000
χ2922-2-2-222-22020-20-2000−2−2222i2i−2i−2i00002i−2i00002-2−2200−i2−i2i2i20000−i2−i2i2i2000000−22000
χ3022-2-2-222-22020-20-2000−2−2222i2i−2i−2i0000−2i2i0000-22−2200i2i2−i2−i20000−i2−i2i2i20000002−2000
χ3122-2-2-222-22020-20-2000−2−222−2i−2i2i2i00002i−2i0000-22−2200−i2−i2i2i20000i2i2−i2−i20000002−2000
χ3222-2-2-222-22020-20-2000−2−222−2i−2i2i2i0000−2i2i00002-2−2200i2i2−i2−i20000i2i2−i2−i2000000−22000
χ332-2-22-22-2222-2-222-2-22-20000000000000000000000002-22-22i2i−2i−2i0000002i−2i0000000
χ342-2-22-22-2222-2-222-2-22-20000000000000000000000002-22-2−2i−2i2i2i000000−2i2i0000000
χ352-2-22-22-2222-2-222-2-22-2000000000000000000000000-22-222i2i−2i−2i000000−2i2i0000000
χ362-2-22-22-2222-2-222-2-22-2000000000000000000000000-22-22−2i−2i2i2i0000002i−2i0000000
χ372-2-2-22-2220-20-20202002-22-22−22−22-22-200000000002−200002−22−22−22−200002−200000
χ382-2-2-22-2220-20-20202002-22-22−22−2-22-2200000000002−20000−22−222−22−20000−2200000
χ392-2-2-22-2220-20-20202002-22-2−22−222-22-20000000000−220000−22−22−22−220000−2200000
χ402-2-2-22-2220-20-20202002-22-2−22−22-22-220000000000−2200002−22−2−22−2200002−200000
χ412-2-2-22-2220-20-2020200-22-222−22−22-2-2200000000002−200002−22−2−22−220000−2200000
χ422-2-2-22-2220-20-2020200-22-222−22−2-222-200000000002−20000−22−22−22−2200002−200000
χ432-2-2-22-2220-20-2020200-22-22−22−222-2-220000000000−220000−22−222−22−200002−200000
χ442-2-2-22-2220-20-2020200-22-22−22−22-222-20000000000−2200002−22−22−22−20000−2200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-44040-40-40400000000000000004i−4i0000000000000000000000000000000
χ47444-4-4-4-44040-40-4040000000000000000−4i4i0000000000000000000000000000000
χ48444-4-4-4-440-404040-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ49444-4-4-4-440-404040-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ5044-4-4-444-4-40-404040002222−22−220000000000000000−22220000000000000000000000000
χ5144-4-4-444-4-40-40404000−22−222222000000000000000022−220000000000000000000000000
χ524-444-4-44-4000000000022−22−22222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ534-444-4-44-4000000000022−22−2222−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ544-444-4-44-40000000000−222222−222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ554-444-4-44-40000000000−222222−22−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ564-44-444-4-440-40-4040000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ574-44-444-4-440-40-404000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ584-44-444-4-4-404040-400000000000000000004i−4i00000000000000000000000000000
χ594-44-444-4-4-404040-40000000000000000000−4i4i00000000000000000000000000000
χ604-4-44-44-444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ614-4-44-44-44-444-4-444-4-4400000000000000000000000000000000000000000000000
χ624-4-44-44-44-4-444-4-4444-400000000000000000000000000000000000000000000000
χ634-4-4-44-44404040-40-400000022−2222−2200000000000000−222200000000000000000000000
χ644-4-4-44-44404040-40-4000000−2222−22220000000000000022−2200000000000000000000000
χ6588-888-8-8-8000000000000000000000000000000000000000000000000000000000

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