Finite Group Databasebeta

← Group #313264

Character table — Group #313264

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-111-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-111-1-1111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1-111-1-1-1-1-1-1-11111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-11-1-1-1-111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-11-1-111111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111111-1-11111-1-1-1-1-11
χ17222222222-22-22-22-2-2-222220000-2-2-2-200000000000000002222-2-20000000000000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-20000000000000000-2-2-2-2220000000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200002222000000000000000022-2-2-220000000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000022220000000000000000-2-2222-20000000000000000
χ2122222222-22-22-22-22-2-2000022220000-2-2-2-20000000022-2-2000000200-2000000000000
χ2222222222-22-22-22-22-2-2000022220000-2-2-2-200000000-2-222000000-2002000000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-2000022220000000022-2-2000000-2002000000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-20000222200000000-2-222000000200-2000000000000
χ25222-2-2-22-2-20-202020002i2i−2i−2i22−2−2000022−2−2i2i2i2i2−i2−i2−i2−i200002i−2i2-20000000000i2−i2002−200
χ26222-2-2-22-2-20-202020002i2i−2i−2i22−2−2000022−2−2i2i2i2i2−i2−i2−i2−i20000−2i2i-220000000000−i2i200−2200
χ27222-2-2-22-2-20-202020002i2i−2i−2i−2−2220000−2−222−i2−i2−i2−i2i2i2i2i200002i−2i2-20000000000−i2i200−2200
χ28222-2-2-22-2-20-202020002i2i−2i−2i−2−2220000−2−222−i2−i2−i2−i2i2i2i2i20000−2i2i-220000000000i2−i2002−200
χ29222-2-2-22-2-20-20202000−2i−2i2i2i22−2−2000022−2−2−i2−i2−i2−i2i2i2i2i200002i−2i-220000000000i2−i200−2200
χ30222-2-2-22-2-20-20202000−2i−2i2i2i22−2−2000022−2−2−i2−i2−i2−i2i2i2i2i20000−2i2i2-20000000000−i2i2002−200
χ31222-2-2-22-2-20-20202000−2i−2i2i2i−2−2220000−2−222i2i2i2i2−i2−i2−i2−i200002i−2i-220000000000−i2i2002−200
χ32222-2-2-22-2-20-20202000−2i−2i2i2i−2−2220000−2−222i2i2i2i2−i2−i2−i2−i20000−2i2i2-20000000000i2−i200−2200
χ332-22-2-22-2222-2-222-2-2-222i−2i2i−2i00002i2i−2i−2i0000000000002i−2i2i−2i0000000000002-200000000
χ342-22-2-22-2222-2-222-2-2-222i−2i2i−2i00002i2i−2i−2i000000000000−2i2i−2i2i000000000000-2200000000
χ352-22-2-22-2222-2-222-2-2-22−2i2i−2i2i0000−2i−2i2i2i0000000000002i−2i2i−2i000000000000-2200000000
χ362-22-2-22-2222-2-222-2-2-22−2i2i−2i2i0000−2i−2i2i2i000000000000−2i2i−2i2i0000000000002-200000000
χ372-22-2-22-222-2-222-2-222-22i−2i2i−2i0000−2i−2i2i2i000000000000000000000002i−2i02-20000000000
χ382-22-2-22-222-2-222-2-222-22i−2i2i−2i0000−2i−2i2i2i00000000000000000000000−2i2i0-220000000000
χ392-22-2-22-222-2-222-2-222-2−2i2i−2i2i00002i2i−2i−2i000000000000000000000002i−2i0-220000000000
χ402-22-2-22-222-2-222-2-222-2−2i2i−2i2i00002i2i−2i−2i00000000000000000000000−2i2i02-20000000000
χ412-22-2-22-22-222-2-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i2i−2i−2i2i00000000000000002-20000
χ422-22-2-22-22-222-2-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i−2i2i2i−2i0000000000000000-220000
χ432-22-2-22-22-222-2-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i2i−2i−2i2i0000000000000000-220000
χ442-22-2-22-22-222-2-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i2i2i−2i00000000000000002-20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-400000002222−22−220000−22−2222220000000000000000000000000000000000
χ47444-4-4-44-44040-40-40000000−22−22222200002222−22−220000000000000000000000000000000000
χ4844-44-44-4-4040-40-40400000000000000000022−2222−2222−2222−2200000000000000000000000000
χ4944-44-44-4-4040-40-404000000000000000000−2222−2222−2222−222200000000000000000000000000
χ5044-44-44-4-40-404040-40000004-44-4000000000000000000000000000000000000000000
χ5144-44-44-4-40-404040-4000000-44-44000000000000000000000000000000000000000000
χ5244-4-44-4-440000000000000022−22−22222i2−2i22i2−2i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5344-4-44-4-440000000000000022−22−2222−2i22i2−2i22i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5444-4-44-4-4400000000000000−222222−222i2−2i22i2−2i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5544-4-44-4-4400000000000000−222222−22−2i22i2−2i22i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ564-4444-4-4-440-40-40400000000000000000002222−22−22−22−22222200000000000000000000000000
χ574-4444-4-4-440-40-4040000000000000000000−22−2222222222−22−2200000000000000000000000000
χ584-4444-4-4-4-404040-40004-4-440000000000000000000000000000000000000000000000
χ594-4444-4-4-4-404040-4000-444-40000000000000000000000000000000000000000000000
χ604-44-4-44-44-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ614-4-44-4-44400000000000000000022−22−222222−2222−222-2-22-222-200000000000000000000000000
χ624-4-44-4-44400000000000000000022−22−2222−2222−2222-222-22-2-2200000000000000000000000000
χ634-4-44-4-444000000000000000000−222222−2222−2222−22-222-22-2-2200000000000000000000000000
χ644-4-44-4-444000000000000000000−222222−22−2222−22222-2-22-222-200000000000000000000000000
χ654-4-4-4444-404040-40-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ664-4-4-4444-404040-40-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ674-4-4-4444-40-40-40404000000000000004-4-440000000000000000000000000000000000
χ684-4-4-4444-40-40-4040400000000000000-444-40000000000000000000000000000000000

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