Finite Group Databasebeta

← Group #278312

Character table — Group #278312

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488884444888888888888888888888888824884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-111-1-11-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111-1-111-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ71111111111111111-1-111-1-11-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111-1-111-1-11-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11
χ11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-11-1
χ13111111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ14111111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1
χ15111111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-111-1
χ16111111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ1722222222-2-222222222-2-2-2-2-2-2-222-2-2220000-2-2-2220000000000000000000000000000
χ1822222222-2-2222222-2-2-2-222-222-2-2-2-2220000-222-2-20000000000000000000000000000
χ1922222222-2-222-2-2-2-222-2-2-2-2-2-2-22222-2-20000222-2-20000000000000000000000000000
χ2022222222-2-222-2-2-2-2-2-2-2-222-222-2-222-2-200002-2-2220000000000000000000000000000
χ212222-2-22-2222-20000222-2-2-2-222-2-2000000000000022-2-200000000000000002-2000000
χ222222-2-22-2222-20000222-2-2-2-222-2-20000000000000-2-2220000000000000000-22000000
χ232222-2-22-2222-20000-2-22-222-2-2-222000000000000022-2-20000000000000000-22000000
χ242222-2-22-2222-20000-2-22-222-2-2-2220000000000000-2-22200000000000000002-2000000
χ252222-2-22-2-2-22-2000022-22222-2-2-2-200002i2i−2i−2i0000000000000000000000000002i−2i0000
χ262222-2-22-2-2-22-2000022-22222-2-2-2-20000−2i−2i2i2i000000000000000000000000000−2i2i0000
χ272222-2-22-2-2-22-20000-2-2-22-2-22222200002i2i−2i−2i000000000000000000000000000−2i2i0000
χ282222-2-22-2-2-22-20000-2-2-22-2-2222220000−2i−2i2i2i0000000000000000000000000002i−2i0000
χ292222-2-2-2222-22222200-2200-2000022-2-20000-2000000000000000022-2-222-2-200000000
χ302222-2-2-2222-22222200-2200-2000022-2-20000-20000000000000000-2-222-2-22200000000
χ312222-2-2-2222-22-2-2-2-200-2200-20000-2-22200002000000000000000022-2-2-2-22200000000
χ322222-2-2-2222-22-2-2-2-200-2200-20000-2-222000020000000000000000-2-22222-2-200000000
χ332222-2-2-22-2-2-222222002-20020000-2-2-2-200002000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ342222-2-2-22-2-2-222222002-20020000-2-2-2-20000200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ352222-2-2-22-2-2-22-2-2-2-2002-2002000022220000-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ362222-2-2-22-2-2-22-2-2-2-2002-2002000022220000-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ372-2-222-2-22002-22i2i−2i−2i2-200000002-2002i−2i00000002i−2i00002−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ382-2-222-2-22002-22i2i−2i−2i2-200000002-2002i−2i00000002i−2i0000−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000
χ392-2-222-2-22002-22i2i−2i−2i-220000000-22002i−2i0000000−2i2i00002−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ402-2-222-2-22002-22i2i−2i−2i-220000000-22002i−2i0000000−2i2i0000−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000
χ412-2-222-2-22002-2−2i−2i2i2i2-200000002-200−2i2i0000000−2i2i00002−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ422-2-222-2-22002-2−2i−2i2i2i2-200000002-200−2i2i0000000−2i2i0000−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000
χ432-2-222-2-22002-2−2i−2i2i2i-220000000-2200−2i2i00000002i−2i00002−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ442-2-222-2-22002-2−2i−2i2i2i-220000000-2200−2i2i00000002i−2i0000−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000
χ452-2-22-222200-2-22i2i−2i−2i00002i−2i02i−2i0000−2i2i000002-2000000i2−i2−i2i2−222−22−2−22i2−i2−i2i200000000
χ462-2-22-222200-2-22i2i−2i−2i00002i−2i02i−2i0000−2i2i000002-2000000−i2i2i2−i22−2−22−222−2−i2i2i2−i200000000
χ472-2-22-222200-2-22i2i−2i−2i0000−2i2i0−2i2i0000−2i2i00000-22000000i2−i2−i2i2−222−2−222−2−i2i2i2−i200000000
χ482-2-22-222200-2-22i2i−2i−2i0000−2i2i0−2i2i0000−2i2i00000-22000000−i2i2i2−i22−2−222−2−22i2−i2−i2i200000000
χ492-2-22-222200-2-2−2i−2i2i2i00002i−2i02i−2i00002i−2i00000-22000000i2−i2−i2i22−2−222−2−22−i2i2i2−i200000000
χ502-2-22-222200-2-2−2i−2i2i2i00002i−2i02i−2i00002i−2i00000-22000000−i2i2i2−i2−222−2−222−2i2−i2−i2i200000000
χ512-2-22-222200-2-2−2i−2i2i2i0000−2i2i0−2i2i00002i−2i000002-2000000i2−i2−i2i22−2−22−222−2i2−i2−i2i200000000
χ522-2-22-222200-2-2−2i−2i2i2i0000−2i2i0−2i2i00002i−2i000002-2000000−i2i2i2−i2−222−22−2−22−i2i2i2−i200000000
χ53444444-4-444-4-4000000-4-4004000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000004400-4000000000000000000000000000000000000000000000
χ554-44-400004-4002i2−2i22i2−2i2000000000002i2−2i2002-22-200000002i2−2i2000000000000000000000000
χ564-44-400004-4002i2−2i22i2−2i2000000000002i2−2i200-22-220000000−2i22i2000000000000000000000000
χ574-44-400004-400−2i22i2−2i22i200000000000−2i22i2002-22-20000000−2i22i2000000000000000000000000
χ584-44-400004-400−2i22i2−2i22i200000000000−2i22i200-22-2200000002i2−2i2000000000000000000000000
χ594-44-40000-44002i2−2i22i2−2i200000000000−2i22i2002i−2i−2i2i0000022−2200000000000000000000000000
χ604-44-40000-44002i2−2i22i2−2i200000000000−2i22i200−2i2i2i−2i00000−222200000000000000000000000000
χ614-44-40000-4400−2i22i2−2i22i2000000000002i2−2i2002i−2i−2i2i00000−222200000000000000000000000000
χ624-44-40000-4400−2i22i2−2i22i2000000000002i2−2i200−2i2i2i−2i0000022−2200000000000000000000000000
χ634-4-444-44-400-44000000004i−4i0−4i4i0000000000000000000000000000000000000000000
χ644-4-444-44-400-4400000000−4i4i04i−4i0000000000000000000000000000000000000000000
χ654-4-44-44-4-4004400004-40000000-4400000000000000000000000000000000000000000
χ664-4-44-44-4-400440000-4400000004-400000000000000000000000000000000000000000
χ6788-8-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ6888-8-800000000−424242−420000000000000000000000000000000000000000000000000000

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