Finite Group Databasebeta

← Group #317618

Character table — Group #317618

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ9111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ172222222222-2-2-2-222-2-222-2-22222-2-2-2-22-20000000022-2-2000000000000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-2-2-222222-200000000-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2222222-2-2-2-2-2200000000-2-222000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-222-2-2-2-22222-220000000022-2-2000000000000000000000000
χ2122222222-2-22222-2-2-2-2222200000000-2-222-2-2-2-2220000000000000000000000000000
χ2222222222-2-22222-2-2-2-2222200000000-2-2-2-22222-2-20000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200000000222222-2-2-2-20000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000000022-2-2-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-220000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-22000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222000000002-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222000000002-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-22-2-2-2-222-2-2222-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22i−2i0000000000
χ30222-2-22-2-2-2-222-2-2222-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22−2i2i0000000000
χ31222-2-22-2-2-2-222-2-2222-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-2−2i2i0000000000
χ32222-2-22-2-2-2-222-2-2222-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-222i−2i0000000000
χ33222-2-22-2-2-2-2-2-22222-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000002-200002i−2i00000000
χ34222-2-22-2-2-2-2-2-22222-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000000-220000−2i2i00000000
χ35222-2-22-2-2-2-2-2-22222-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000002-20000−2i2i00000000
χ36222-2-22-2-2-2-2-2-22222-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000-2200002i−2i00000000
χ372-2-22-222-2002-22-200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200002-22i−2i002−22−22−22−2i2−i2i2−i20000000000000000
χ382-2-22-222-2002-22-200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000-22−2i2i002−22−2−22−22−i2i2−i2i20000000000000000
χ392-2-22-222-2002-22-200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200002-22i−2i00−22−22−22−22−i2i2−i2i20000000000000000
χ402-2-22-222-2002-22-200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000-22−2i2i00−22−222−22−2i2−i2i2−i20000000000000000
χ412-2-22-222-2002-22-20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200002-2−2i2i00−22−22−22−22i2−i2i2−i20000000000000000
χ422-2-22-222-2002-22-20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000-222i−2i00−22−222−22−2−i2i2−i2i20000000000000000
χ432-2-22-222-2002-22-20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200002-2−2i2i002−22−22−22−2−i2i2−i2i20000000000000000
χ442-2-22-222-2002-22-20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000-222i−2i002−22−2−22−22i2−i2i2−i20000000000000000
χ452-2-22-222-200-22-2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2002-200002i−2i2−2−22i2−i2−i2i2−222−20000000000000000
χ462-2-22-222-200-22-2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200-220000−2i2i2−2−22−i2i2i2−i22−2−220000000000000000
χ472-2-22-222-200-22-2200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2002-200002i−2i−222−2−i2i2i2−i22−2−220000000000000000
χ482-2-22-222-200-22-2200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i200-220000−2i2i−222−2i2−i2−i2i2−222−20000000000000000
χ492-2-22-222-200-22-220000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2002-20000−2i2i−222−2i2−i2−i2i22−2−220000000000000000
χ502-2-22-222-200-22-220000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i200-2200002i−2i−222−2−i2i2i2−i2−222−20000000000000000
χ512-2-22-222-200-22-220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2002-20000−2i2i2−2−22−i2i2i2−i2−222−20000000000000000
χ522-2-22-222-200-22-220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200-2200002i−2i2−2−22i2−i2−i2i22−2−220000000000000000
χ53444-4-44-4-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ54444-4-44-4-444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ5544-444-4-4-44-400004-400000000000000000000000000000000000000000000000022−2200
χ5644-444-4-4-44-400004-4000000000000000000000000000000000000000000000000−222200
χ5744-444-4-4-4-440000-440000000000000000000000000000000000000000000000000022−22
χ5844-444-4-4-4-440000-4400000000000000000000000000000000000000000000000000−2222
χ5944-4-4-4-4444-40000-44000000000000000000000000000000000000000000000022−220000
χ6044-4-4-4-4444-40000-440000000000000000000000000000000000000000000000−22220000
χ6144-4-4-4-444-4400004-40000000000000000000000000000000000000000000022−22000000
χ6244-4-4-4-444-4400004-400000000000000000000000000000000000000000000−2222000000
χ634-4-4-444-44004-4-440000000022−22−222222−22−222200000000000000000000000000000000000000
χ644-4-4-444-44004-4-4400000000−222222−22−222222−2200000000000000000000000000000000000000
χ654-4-4-444-4400-444-40000000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-444-4400-444-400000000−222222−2222−22−222200000000000000000000000000000000000000
χ678-888-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-88-88-8000000000000000000000000000000000000000000000000000000000000

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