Finite Group Databasebeta

← Group #341555

Character table — Group #341555

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1111111-1-11-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-11111-1-1-1-11111111111-1-1-11-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-111-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11111111-1
χ9111111111111111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1111-1-1
χ11111111111111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1-1-1111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-111111111-1-1-1-1-11-1
χ17222222222-22-22-22-2-2-22222000022220000-2-2000000000000-2-2000000-200000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-2000022000000000000-2-2000000200000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000022-2-20000-2-200000000000022000000200000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000-2-22200002200000000000022000000-200000000
χ2122222222-22-22-22-22-2-2000022220000222200-2-2-2-200000000000000000-20000000
χ2222222222-22-22-22-22-2-2000022220000-2-2-2-20022-2-20000000000000000020000000
χ2322222222-22-22-22-22-2-20000-2-2-2-2000022-2-200-2-2220000000000000000020000000
χ2422222222-22-22-22-22-2-20000-2-2-2-20000-2-22200222200000000000000000-20000000
χ25222-2-22-2-222-2-222-2-22-2000000000000000000000022-2-222-2-20000002-2000000000
χ26222-2-22-2-222-2-222-2-22-2000000000000000000000022-2-2-2-222000000-22000000000
χ27222-2-22-2-222-2-222-2-22-20000000000000000000000-2-22222-2-2000000-22000000000
χ28222-2-22-2-222-2-222-2-22-20000000000000000000000-2-222-2-2220000002-2000000000
χ2922-222-2-2-22020-20-200022-2-222−2−22-22-2000000002−22−22−200000022−2−200002−200000
χ3022-222-2-2-22020-20-200022-2-222−2−2-22-22000000002−2−22−2200000022−2−20000−2200000
χ3122-222-2-2-22020-20-200022-2-2−2−2222-22-200000000−22−22−22000000−2−2220000−2200000
χ3222-222-2-2-22020-20-200022-2-2−2−222-22-2200000000−222−22−2000000−2−22200002−200000
χ3322-222-2-2-22020-20-2000-2-22222−2−22-2-22000000002−22−22−2000000−2−2220000−2200000
χ3422-222-2-2-22020-20-2000-2-22222−2−2-222-2000000002−2−22−22000000−2−22200002−200000
χ3522-222-2-2-22020-20-2000-2-222−2−2222-2-2200000000−22−22−2200000022−2−200002−200000
χ3622-222-2-2-22020-20-2000-2-222−2−222-222-200000000−222−22−200000022−2−20000−2200000
χ372-2-22-222-2020-20-20200i2−i2i2−i22-22-200002-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2000000i2−i2000
χ382-2-22-222-2020-20-20200i2−i2i2−i22-22-20000-22-220000000000−i2i2−i2i2i2−i2i2−i2i2−i2000000−i2i2000
χ392-2-22-222-2020-20-20200i2−i2i2−i2-22-2200002-2-220000000000i2−i2i2−i2i2−i2−i2i2−i2i2000000−i2i2000
χ402-2-22-222-2020-20-20200i2−i2i2−i2-22-220000-222-20000000000−i2i2−i2i2i2−i2−i2i2−i2i2000000i2−i2000
χ412-2-22-222-2020-20-20200−i2i2−i2i22-22-200002-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2000000−i2i2000
χ422-2-22-222-2020-20-20200−i2i2−i2i22-22-20000-22-220000000000i2−i2i2−i2−i2i2−i2i2−i2i2000000i2−i2000
χ432-2-22-222-2020-20-20200−i2i2−i2i2-22-2200002-2-220000000000−i2i2−i2i2−i2i2i2−i2i2−i2000000i2−i2000
χ442-2-22-222-2020-20-20200−i2i2−i2i2-22-220000-222-20000000000i2−i2i2−i2−i2i2i2−i2i2−i2000000−i2i2000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-44-4-44-4-444-4-44-4400000000000000000000000000000000000000000000000
χ47444-4-44-4-4-444-4-444-4-4400000000000000000000000000000000000000000000000
χ48444-4-44-4-4-4-444-4-4444-400000000000000000000000000000000000000000000000
χ4944-444-4-4-4-40-4040400000002222−22−22000000000000−22220000000000000000000000000
χ5044-444-4-4-4-40-404040000000−22−22222200000000000022−220000000000000000000000000
χ5144-4-4-4-44440-40-404000000000000000000000000022−22−2222000000000000000000000
χ5244-4-4-4-44440-40-4040000000000000000000000000−222222−22000000000000000000000
χ5344-4-4-4-444-404040-400000000000000000004-400000000000000000000000000000
χ5444-4-4-4-444-404040-40000000000000000000-4400000000000000000000000000000
χ554-444-4-4-4400000000002i2−2i2−2i22i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ564-444-4-4-4400000000002i2−2i2−2i22i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ574-444-4-4-440000000000−2i22i22i2−2i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ584-444-4-4-440000000000−2i22i22i2−2i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ594-4-44-444-40-404040-4002i2−2i22i2−2i200000000000000000000000000−2i22i2000000000000000
χ604-4-44-444-40-404040-400−2i22i2−2i22i2000000000000000000000000002i2−2i2000000000000000
χ614-4-4-444-4404040-40-400000000000000000000000000002i2−2i2−2i22i200000000000000000
χ624-4-4-444-4404040-40-40000000000000000000000000000−2i22i22i2−2i200000000000000000
χ634-4-4-444-440-40-40404000000000000000000004-4000000000000000000000000000
χ644-4-4-444-440-40-4040400000000000000000000-44000000000000000000000000000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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