Finite Group Databasebeta

← Group #278303

Character table — Group #278303

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488884444888888888888888888888888824884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-111-1-1-1-11-1-1111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111-1-111-1-1-1-11-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ71111111111111111-1-111-1-1-1-11-1-11111-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111-1-111-1-1-1-11-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ9111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-11-11
χ11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111-1-11-11-1
χ13111111111111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-111-1
χ14111111111111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11111-111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-11-1-11
χ15111111111111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1111-1-11
χ16111111111111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-111-111-1
χ1722222222-222-2222222-2-2-2-222-2-2-2-2-2220000-2-2-2000000002200000000000000000000
χ1822222222-222-22222-2-2-2-222-2-2-222-2-2220000-22200000000-2-200000000000000000000
χ1922222222-222-2-2-2-2-222-2-2-2-222-2-2-222-2-2000022200000000-2-200000000000000000000
χ2022222222-222-2-2-2-2-2-2-2-2-222-2-2-22222-2-200002-2-2000000002200000000000000000000
χ212222-2-22-222-220000222-2-2-2-2-2-2220000000000022-2-20000000000000000002-2000000
χ222222-2-22-222-220000222-2-2-2-2-2-22200000000000-2-222000000000000000000-22000000
χ232222-2-22-222-220000-2-22-22222-2-2-20000000000022-2-2000000000000000000-22000000
χ242222-2-22-222-220000-2-22-22222-2-2-200000000000-2-2220000000000000000002-2000000
χ252222-2-22-2-22-2-2000022-2222-2-22-2-200002i2i−2i−2i0000000000000000000000000002i−2i0000
χ262222-2-22-2-22-2-2000022-2222-2-22-2-20000−2i−2i2i2i000000000000000000000000000−2i2i0000
χ272222-2-22-2-22-2-20000-2-2-22-2-22222200002i2i−2i−2i000000000000000000000000000−2i2i0000
χ282222-2-22-2-22-2-20000-2-2-22-2-2222220000−2i−2i2i2i0000000000000000000000000002i−2i0000
χ292222-2-2-222-222222200-220000-20022-2-20000-2000000222200-2-2-2-20000000000000000
χ302222-2-2-222-222222200-220000-20022-2-20000-2000000-2-2-2-20022220000000000000000
χ312222-2-2-222-222-2-2-2-200-220000-200-2-2220000200000022-2-200-2-2220000000000000000
χ322222-2-2-222-222-2-2-2-200-220000-200-2-22200002000000-2-2220022-2-20000000000000000
χ332222-2-2-22-2-22-22222002-20000200-2-2-2-20000200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ342222-2-2-22-2-22-22222002-20000200-2-2-2-2000020000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ352222-2-2-22-2-22-2-2-2-2-2002-2000020022220000-200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ362222-2-2-22-2-22-2-2-2-2-2002-2000020022220000-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ372-22-22-2-2-2022022-2-200002i−2i0002i−2i002-2000002i−2i0000i2−i2i2−i200i2−i2i2−i22−22−22−22−200000000
χ382-22-22-2-2-2022022-2-200002i−2i0002i−2i002-2000002i−2i0000−i2i2−i2i200−i2i2−i2i2−22−22−22−2200000000
χ392-22-22-2-2-2022022-2-20000−2i2i000−2i2i002-200000−2i2i0000i2−i2i2−i200i2−i2i2−i2−22−22−22−2200000000
χ402-22-22-2-2-2022022-2-20000−2i2i000−2i2i002-200000−2i2i0000−i2i2−i2i200−i2i2−i2i22−22−22−22−200000000
χ412-22-22-2-2-20220-2-22200002i−2i0002i−2i00-2200000−2i2i0000i2−i2−i2i200i2−i2−i2i22−22−2−22−2200000000
χ422-22-22-2-2-20220-2-22200002i−2i0002i−2i00-2200000−2i2i0000−i2i2i2−i200−i2i2i2−i2−22−222−22−200000000
χ432-22-22-2-2-20220-2-2220000−2i2i000−2i2i00-22000002i−2i0000i2−i2−i2i200i2−i2−i2i2−22−222−22−200000000
χ442-22-22-2-2-20220-2-2220000−2i2i000−2i2i00-22000002i−2i0000−i2i2i2−i200−i2i2i2−i22−22−2−22−2200000000
χ452-22-2-222-20-22022-2-22-200002-200000-2200000000000i2−i2i2−i22-2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ462-22-2-222-20-22022-2-22-200002-200000-2200000000000−i2i2−i2i22-2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ472-22-2-222-20-22022-2-2-220000-2200000-2200000000000i2−i2i2−i2-22−i2i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ482-22-2-222-20-22022-2-2-220000-2200000-2200000000000−i2i2−i2i2-22i2−i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ492-22-2-222-20-220-2-2222-200002-2000002-200000000000i2−i2−i2i2-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ502-22-2-222-20-220-2-2222-200002-2000002-200000000000−i2i2i2−i2-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ512-22-2-222-20-220-2-222-220000-22000002-200000000000i2−i2−i2i22-2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ522-22-2-222-20-220-2-222-220000-22000002-200000000000−i2i2i2−i22-2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ53444444-4-44-4-44000000-4-4000040000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-4000000440000-40000000000000000000000000000000000000000000
χ554-44-44-4440-4-4000004-40000-4400000000000000000000000000000000000000000000
χ564-44-44-4440-4-400000-4400004-400000000000000000000000000000000000000000000
χ574-44-4-44-4404-40000000004i−4i000−4i4i00000000000000000000000000000000000000000
χ584-44-4-44-4404-4000000000−4i4i0004i−4i00000000000000000000000000000000000000000
χ594-4-440000400-422−2222−220000000000022−22002i−2i2i−2i000002i2−2i200000000000000000000000000
χ604-4-440000400-422−2222−220000000000022−2200−2i2i−2i2i00000−2i22i200000000000000000000000000
χ614-4-440000400-4−2222−222200000000000−2222002i−2i2i−2i00000−2i22i200000000000000000000000000
χ624-4-440000400-4−2222−222200000000000−222200−2i2i−2i2i000002i2−2i200000000000000000000000000
χ634-4-440000-400422−2222−2200000000000−2222002-2-2200022−220000000000000000000000000000
χ644-4-440000-400422−2222−2200000000000−222200-222-2000−22220000000000000000000000000000
χ654-4-440000-4004−2222−22220000000000022−22002-2-22000−22220000000000000000000000000000
χ664-4-440000-4004−2222−22220000000000022−2200-222-200022−220000000000000000000000000000
χ6788-8-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ6888-8-800000000−424242−420000000000000000000000000000000000000000000000000000

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