Finite Group Databasebeta

← Group #337697

Character table — Group #337697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888824448888224
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1111111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1
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
χ51111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-11-11
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-111-1-111-11-1
χ71111111111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-111111-11
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
χ10111111111111111111-1-1-1-1111111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ11111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-11
χ17222222222-22-22-22-2-2-20000222222000000-2-22200-2-2000000000000-20000000000
χ18222222222-22-22-22-2-2-200002222-2-200000022-2-200-2-200000000000020000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-222000000-2-2-2-2002200000000000020000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2-2-200000022220022000000000000-20000000000
χ2122222222-22-22-22-22-2-2222200000022-2-2-2-20000-2-20000000000000002000000000
χ2222222222-22-22-22-22-2-22222000000-2-222220000-2-2000000000000000-2000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000002222-2-2000022000000000000000-2000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000-2-2-2-2220000220000000000000002000000000
χ25222-2-2-2-2222-2-222-2-22-200000000000000000000000022-2-22i2i−2i−2i0000002i−2i0000000
χ26222-2-2-2-2222-2-222-2-22-200000000000000000000000022-2-2−2i−2i2i2i000000−2i2i0000000
χ27222-2-2-2-2222-2-222-2-22-2000000000000000000000000-2-2222i2i−2i−2i000000−2i2i0000000
χ28222-2-2-2-2222-2-222-2-22-2000000000000000000000000-2-222−2i−2i2i2i0000002i−2i0000000
χ2922-222-2-2-2-202020-2000i2i2−i2−i22i2i−2i−2i2-2000000002i−2ii2−i2000000i2−i2i2−i222−2−200002−200000
χ3022-222-2-2-2-202020-2000i2i2−i2−i22i2i−2i−2i-2200000000−2i2ii2−i2000000−i2i2−i2i222−2−20000−2200000
χ3122-222-2-2-2-202020-2000i2i2−i2−i2−2i−2i2i2i2-200000000−2i2ii2−i2000000i2−i2i2−i2−2−2220000−2200000
χ3222-222-2-2-2-202020-2000i2i2−i2−i2−2i−2i2i2i-22000000002i−2ii2−i2000000−i2i2−i2i2−2−22200002−200000
χ3322-222-2-2-2-202020-2000−i2−i2i2i22i2i−2i−2i2-2000000002i−2i−i2i2000000−i2i2−i2i2−2−2220000−2200000
χ3422-222-2-2-2-202020-2000−i2−i2i2i22i2i−2i−2i-2200000000−2i2i−i2i2000000i2−i2i2−i2−2−22200002−200000
χ3522-222-2-2-2-202020-2000−i2−i2i2i2−2i−2i2i2i2-200000000−2i2i−i2i2000000−i2i2−i2i222−2−200002−200000
χ3622-222-2-2-2-202020-2000−i2−i2i2i2−2i−2i2i2i-22000000002i−2i−i2i2000000i2−i2i2−i222−2−20000−2200000
χ372-2-22-2-2220-20-20202002-22-22−22−200002-22-20000002−22−22−200002−22−20000002−2000
χ382-2-22-2-2220-20-20202002-22-22−22−20000-22-220000002−2−22−2200002−22−2000000−22000
χ392-2-22-2-2220-20-20202002-22-2−22−2200002-22-2000000−22−22−220000−22−22000000−22000
χ402-2-22-2-2220-20-20202002-22-2−22−220000-22-22000000−222−22−20000−22−220000002−2000
χ412-2-22-2-2220-20-2020200-22-222−22−200002-2-220000002−2−22−220000−22−220000002−2000
χ422-2-22-2-2220-20-2020200-22-222−22−20000-222-20000002−22−22−20000−22−22000000−22000
χ432-2-22-2-2220-20-2020200-22-22−22−2200002-2-22000000−222−22−200002−22−2000000−22000
χ442-2-22-2-2220-20-2020200-22-22−22−220000-222-2000000−22−22−2200002−22−20000002−2000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ47444-4-4-4-44-444-4-444-4-4400000000000000000000000000000000000000000000000
χ48444-4-4-4-44-4-444-4-4444-400000000000000000000000000000000000000000000000
χ4944-444-4-4-440-40-4040002i22i2−2i2−2i20000000000000000−2i22i20000000000000000000000000
χ5044-444-4-4-440-40-404000−2i2−2i22i22i200000000000000002i2−2i20000000000000000000000000
χ5144-4-4-444-44040-40-400000000000000000004i−4i00000000000000000000000000000
χ5244-4-4-444-44040-40-40000000000000000000−4i4i00000000000000000000000000000
χ5344-4-4-444-4-40-40404000000000000000000000000000000022−22−2222000000000000000
χ5444-4-4-444-4-40-404040000000000000000000000000000000−222222−22000000000000000
χ554-444-44-4-400000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000002-2-2200000000000
χ564-444-44-4-400000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000-222-200000000000
χ574-444-44-4-40000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000-222-200000000000
χ584-444-44-4-40000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000002-2-2200000000000
χ594-4-44-4-44404040-40-400000022−2222−2200000000000000−222200000000000000000000000
χ604-4-44-4-44404040-40-4000000−2222−22220000000000000022−2200000000000000000000000
χ614-4-4-444-44040-40-4040000000000004-400000000000000000000000000000000000
χ624-4-4-444-44040-40-404000000000000-4400000000000000000000000000000000000
χ634-4-4-444-440-404040-40000000000000000000000000022−22−22220000000000000000000
χ644-4-4-444-440-404040-400000000000000000000000000−222222−220000000000000000000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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