Finite Group Databasebeta

← Group #490041

Character table — Group #490041

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222444444448888888888888888888888888161616161616161632323232
order122222444488884444888824444444816161616161616161616161616161616444444884488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111-1-11-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-111-111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-111-111-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1
χ91111-1-1111111111-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1111-11-11-1
χ101111-1-1111111111-1-1-1-1-1111-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-11-11
χ111111-1-1111111111-1-1-1-1-1111-1-1-1111-1-11111-1-1-1-11111-1-1-1-11-111-1-11-1-11-11
χ121111-1-1111111111-1-1-1-1-1111-1-1-1111-1-1-1-1-1-11111-1-1-1-111111-111-1-11-11-11-1
χ131111-1-1111111111-1-1-1-1-111-1111-1-1-11-11111-1-1-1-1-1-1-1-11111-1111-1-1-111-1-11
χ141111-1-1111111111-1-1-1-1-111-1111-1-1-11-1-1-1-1-111111111-1-1-1-1-1111-1-1-11-111-1
χ151111-1-1111111111-1-1-1-1-111-11-1-1-1111-11111-1-1-1-1-1-1-1-111111-1-1-111-11-111-1
χ161111-1-1111111111-1-1-1-1-111-11-1-1-1111-1-1-1-1-111111111-1-1-1-11-1-1-111-111-1-11
χ172222222222-2-2-2-22222-2-2-2-222002002-20000000000000000000000-2-20000
χ182222222222-2-2-2-22222-2-2-2-2-2-200-200-2-20000000000000000000000220000
χ1922222222-2-22222-2-22-222-2-200220-2-20-200000000000000002-20000000000
χ2022222222-2-22222-2-22-222-2-200-2-20220-20000000000000000-220000000000
χ2122222222-2-2-2-2-2-2-2-22-2-2-2220000000020000000000000000002-22-2000000
χ2222222222-2-2-2-2-2-2-2-22-2-2-222000000002000000000000000000-22-22000000
χ23222222-2-2220000-2-2-2200002200-200-2022−2−222−2−222−2−222−2−2000000000000
χ24222222-2-2220000-2-2-2200002200-200-20−2−222−2−222−2−222−2−222000000000000
χ25222222-2-2220000-2-2-220000-2-2002002022−2−222−2−2−2−222−2−222000000000000
χ26222222-2-2220000-2-2-220000-2-20020020−2−222−2−22222−2−222−2−2000000000000
χ272222-2-22222-2-2-2-22-2-2-222-2-22-200200-220000000000000000000000-220000
χ282222-2-22222-2-2-2-22-2-2-222-2-2-2200-2002200000000000000000000002-20000
χ292222-2-222-2-22222-22-22-2-2-2-20022022020000000000000000-2-20000000000
χ302222-2-222-2-22222-22-22-2-2-2-200-2-20-2-2020000000000000000220000000000
χ312222-2-222-2-2-2-2-2-2-22-22222200000000-20000000000000000002-2-22000000
χ322222-2-222-2-2-2-2-2-2-22-22222200000000-2000000000000000000-222-2000000
χ332222-2-2-2-2220000-222-200002-200-2002022−2−2−2−22222−2−2−2−222000000000000
χ342222-2-2-2-2220000-222-200002-200-20020−2−22222−2−2−2−22222−2−2000000000000
χ352222-2-2-2-2220000-222-20000-2200200-2022−2−2−2−222−2−22222−2−2000000000000
χ362222-2-2-2-2220000-222-20000-2200200-20−2−22222−2−222−2−2−2−222000000000000
χ37444444-4-4-4-4000044-4-400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-400004-44400000000000000000000000000000000000000000
χ3944-4-44-4000022−2222−22000022−220000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000
χ4044-4-44-4000022−2222−22000022−220000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000
χ4144-4-44-40000−2222−22220000−22220000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000
χ4244-4-44-40000−2222−22220000−22220000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000
χ4344-4-4-44000022−2222−220000−22220000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000
χ4444-4-4-44000022−2222−220000−22220000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000
χ4544-4-4-440000−2222−2222000022−220000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000
χ4644-4-4-440000−2222−2222000022−220000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000
χ474-44-4004-40044-4-400000000000004-4000000000000000000000000000000
χ484-44-4004-40044-4-40000000000000-44000000000000000000000000000000
χ494-44-4004-400-4-44400000000004i−4i000000000000000000000000000000000
χ504-44-4004-400-4-4440000000000−4i4i000000000000000000000000000000000
χ514-4-4400004-422−22−222200000022−2200000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000
χ524-4-4400004-422−22−222200000022−220000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000
χ534-4-4400004-4−222222−22000000−222200000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000
χ544-4-4400004-4−222222−22000000−22220000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000
χ554-4-440000-4422−22−2222000000−22220000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000
χ564-4-440000-4422−22−2222000000−2222000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000
χ574-4-440000-44−222222−2200000022−220000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000
χ584-4-440000-44−222222−2200000022−22000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000
χ598-88-800-88000000000000000000000000000000000000000000000000000

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