Finite Group Databasebeta

← Group #506162

Character table — Group #506162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888816161616161616161616161616161616244488881616161616161616444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-111-1
χ9111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-1-11-11
χ10111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1111-11-1
χ11111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-11-11-1
χ12111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-11-11
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000
χ19222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-200000000000000000000
χ20222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-222220000000000000000-2-222-2-22200000000000000000000
χ2122222222-22222-2-2-200000000-2-200002222−2−2−2−22222−2−2−2−22-2-22000022−2−222−2−2000000000000
χ2222222222-22222-2-2-200000000-2-200002222−2−2−2−22222−2−2−2−2-222-20000−2−222−2−222000000000000
χ2322222222-22222-2-2-200000000-2-20000−2−2−2−22222−2−2−2−222222-2-220000−2−222−2−222000000000000
χ2422222222-22222-2-2-200000000-2-20000−2−2−2−22222−2−2−2−22222-222-2000022−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002200002222−2−2−2−2−2−2−2−222222-22-2000022−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002200002222−2−2−2−2−2−2−2−22222-22-220000−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-200000000220000−2−2−2−222222222−2−2−2−22-22-20000−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-200000000220000−2−2−2−222222222−2−2−2−2-22-22000022−2−2−2−222000000000000
χ29222-22-2-2-2-200002-22-2-222-2-2220000000000000022-2-222-2-20000000000000000002i−2i2i−2i000000
χ30222-22-2-2-2-200002-22-2-222-2-2220000000000000022-2-222-2-2000000000000000000−2i2i−2i2i000000
χ31222-22-2-2-2-200002-22-2-222-2-22200000000000000-2-222-2-2220000000000000000002i−2i−2i2i000000
χ32222-22-2-2-2-200002-22-2-222-2-22200000000000000-2-222-2-222000000000000000000−2i2i2i−2i000000
χ332-222-2-22-222i2i−2i−2i-2-2222-2-2-2-2222i−2i2i2i−2i−2i0000000000000000000000002i−2i2i−2i2-22-2000000000000
χ342-222-2-22-222i2i−2i−2i-2-2222-2-2-2-2222i−2i2i2i−2i−2i000000000000000000000000−2i2i−2i2i-22-22000000000000
χ352-222-2-22-222i2i−2i−2i-2-22-2-22222-2-22i−2i−2i−2i2i2i22-2-222-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ362-222-2-22-222i2i−2i−2i-2-22-2-22222-2-22i−2i−2i−2i2i2i-2-222-2-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ372-222-2-22-22−2i−2i2i2i-2-2222-2-2-2-222−2i2i−2i−2i2i2i0000000000000000000000002i−2i2i−2i-22-22000000000000
χ382-222-2-22-22−2i−2i2i2i-2-2222-2-2-2-222−2i2i−2i−2i2i2i000000000000000000000000−2i2i−2i2i2-22-2000000000000
χ392-222-2-22-22−2i−2i2i2i-2-22-2-22222-2-2−2i2i2i2i−2i−2i22-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ402-222-2-22-22−2i−2i2i2i-2-22-2-22222-2-2−2i2i2i2i−2i−2i-2-222-2-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ412-222-2-22-2-22i2i−2i−2i22-200000000−2i2i000022−2−2−2−222i2−i2i2−i2−i2i2−i2i200002-22i−2ii2−i2−i2i22−2−22000000000000
χ422-222-2-22-2-22i2i−2i−2i22-200000000−2i2i000022−2−2−2−222i2−i2i2−i2−i2i2−i2i20000-22−2i2i−i2i2i2−i2−222−2000000000000
χ432-222-2-22-2-22i2i−2i−2i22-200000000−2i2i0000−2−22222−2−2−i2i2−i2i2i2−i2i2−i200002-22i−2i−i2i2i2−i2−222−2000000000000
χ442-222-2-22-2-22i2i−2i−2i22-200000000−2i2i0000−2−22222−2−2−i2i2−i2i2i2−i2i2−i20000-22−2i2ii2−i2−i2i22−2−22000000000000
χ452-222-2-22-2-2−2i−2i2i2i22-2000000002i−2i000022−2−2−2−222−i2i2−i2i2i2−i2i2−i200002-2−2i2i−i2i2i2−i22−2−22000000000000
χ462-222-2-22-2-2−2i−2i2i2i22-2000000002i−2i000022−2−2−2−222−i2i2−i2i2i2−i2i2−i20000-222i−2ii2−i2−i2i2−222−2000000000000
χ472-222-2-22-2-2−2i−2i2i2i22-2000000002i−2i0000−2−22222−2−2i2−i2i2−i2−i2i2−i2i200002-2−2i2ii2−i2−i2i2−222−2000000000000
χ482-222-2-22-2-2−2i−2i2i2i22-2000000002i−2i0000−2−22222−2−2i2−i2i2−i2−i2i2−i2i20000-222i−2i−i2i2i2−i22−2−22000000000000
χ492-22-2-22-22-20000-2222222-2-2-2-2000000000000002i−2i−2i2i2i−2i−2i2i00000000000000002i−2i00002-20000
χ502-22-2-22-22-20000-2222222-2-2-2-2000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000−2i2i0000-220000
χ512-22-2-22-22-20000-2222222-2-2-2-200000000000000−2i2i2i−2i−2i2i2i−2i00000000000000002i−2i0000-220000
χ522-22-2-22-22-20000-2222222-2-2-2-200000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000−2i2i00002-20000
χ53444-44-4-4-440000-44-400000000000000000000002222−22−22−22−2222220000000000000000000000000000
χ54444-44-4-4-440000-44-40000000000000000000000−22−2222222222−22−220000000000000000000000000000
χ55444-44-4-4-4-400004-4444-4-444-4-400000000000000000000000000000000000000000000000000
χ5644-44-4-4-440000000022−2222−2222−2222−220000002ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000000000
χ5744-44-4-4-440000000022−2222−2222−2222−22000000−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000000000
χ5844-44-4-4-4400000000−2222−2222−2222−22220000002ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000000000
χ5944-44-4-4-4400000000−2222−2222−2222−2222000000−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000000000
χ6044-4-4-444-404i−4i4i−4i00022−22−222222−22−2222002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ6144-4-4-444-404i−4i4i−4i000−222222−22−222222−2200−2i22i2−2i22i200000000000000000000000000000000000000000000
χ6244-4-4-444-40−4i4i−4i4i00022−22−222222−22−222200−2i22i2−2i22i200000000000000000000000000000000000000000000
χ6344-4-4-444-40−4i4i−4i4i000−222222−22−222222−22002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ644-44-4-44-44400004-4-400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ654-44-4-44-44400004-4-40000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ664-44-4-44-44-40000-444-4-4-4-4444400000000000000000000000000000000000000000000000000
χ674-4-4444-4-40000000022−22−2222−222222−220000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000000000
χ684-4-4444-4-40000000022−22−2222−222222−22000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000000000
χ694-4-4444-4-400000000−222222−2222−22−22220000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000000000
χ704-4-4444-4-400000000−222222−2222−22−2222000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000000000
χ714-4-4-44-44404-4-4400022−2222−22−2222−22220022−22−222200000000000000000000000000000000000000000000
χ724-4-4-44-44404-4-44000−2222−222222−2222−2200−222222−2200000000000000000000000000000000000000000000
χ734-4-4-44-4440-444-400022−2222−22−2222−222200−222222−2200000000000000000000000000000000000000000000
χ744-4-4-44-4440-444-4000−2222−222222−2222−220022−22−222200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.