Finite Group Databasebeta

← Group #490390

Character table — Group #490390

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222444444444444888888888888888161616161616161616161616161616163232
order12224444448888244444448888448888816161616161616162244444488881616161644
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1-1-11111-1-11-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-11-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111
χ7111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111
χ8111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1
χ91111-1-111111111-11-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11-1111-1-1-111-1-111-1-11-1
χ101111-1-111111111-11-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-11-1-1-1111-1-11111-1-1-11
χ111111-1-111111111-11-1-111-1-1-1-1111-1-111-1-1-1-1-1-111111-1111-1-1-1-1-111-1-111-11
χ121111-1-111111111-11-1-111-1-1-1-1111-1-111-1-1-1-1-1-11111-11-1-1-111111-1-1-1-1111-1
χ131111-1-111111111-11-1-1-1-111-1-111-11-1-1-1111111-1-1-1-11-1-1-11-11111-1-1-1-111-11
χ141111-1-111111111-11-1-1-1-111-1-111-11-1-1-1111111-1-1-1-1-1111-11-1-1-1-111-1-1111-1
χ151111-1-111111111-11-1-1-1-111-1-111-11-1-1-111-1-1-1-111111-1-1-11-111-1-11111-1-11-1
χ161111-1-111111111-11-1-1-1-111-1-111-11-1-1-111-1-1-1-11111-1111-11-1-111-1-111-1-1-11
χ172222222222-2-2-2-222222222-2-2-2-222-2-2-2-2-200000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ192222222-2-2222222-2-2-2000022-2-200-20000000000002-200-22000000000000
χ202222222-2-2222222-2-2-2000022-2-200-2000000000000-22002-2000000000000
χ212222222-2-22-2-2-2-22-2-2-20000-2-222002000000000000002-2002-20000000000
χ222222222-2-22-2-2-2-22-2-2-20000-2-22200200000000000000-2200-220000000000
χ23222222-222-20000-2-22-222-2-20000-220000022−2−222−2−20000000000002−22−200
χ24222222-222-20000-2-22-222-2-20000-2200000−2−222−2−222000000000000−22−2200
χ25222222-222-20000-2-22-2-2-22200002-20000022−2−222−2−2000000000000−22−2200
χ26222222-222-20000-2-22-2-2-22200002-200000−2−222−2−2220000000000002−22−200
χ272222-2-22222-2-2-2-2-22-2-222-2-222-2-22-22-2-22200000000000000000000000000
χ282222-2-22222-2-2-2-2-22-2-2-2-22222-2-2-22222-2-200000000000000000000000000
χ292222-2-22-2-222222-2-2220000-2-2-2-20020000000000002200-2-2000000000000
χ302222-2-22-2-222222-2-2220000-2-2-2-2002000000000000-2-20022000000000000
χ312222-2-22-2-22-2-2-2-2-2-2220000222200-2000000000000002-200-220000000000
χ322222-2-22-2-22-2-2-2-2-2-2220000222200-200000000000000-22002-20000000000
χ332222-2-2-222-200002-2-2222220000-2-20000022−2−2−2−2220000000000002−2−2200
χ342222-2-2-222-200002-2-2222220000-2-200000−2−22222−2−2000000000000−222−200
χ352222-2-2-222-200002-2-22-2-2-2-20000220000022−2−2−2−222000000000000−222−200
χ362222-2-2-222-200002-2-22-2-2-2-200002200000−2−22222−2−20000000000002−2−2200
χ37444444-4-4-4-40000-44-4400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-40000444-400000000000000000000000000000000000000000
χ3944-4-400400-444-4-4000000000000000000000000000000000000022−22000000
χ4044-4-400400-444-4-40000000000000000000000000000000000000−2222000000
χ4144-4-400400-4-4-4440000000000000000000000000000000000022−2200000000
χ4244-4-400400-4-4-44400000000000000000000000000000000000−222200000000
χ434-44-40004-4022−2222−220000004i−4i0022−22000002i2−2i200000000000000000000000000
χ444-44-40004-4022−2222−22000000−4i4i0022−2200000−2i22i200000000000000000000000000
χ454-44-40004-40−2222−22220000004i−4i00−222200000−2i22i200000000000000000000000000
χ464-44-40004-40−2222−2222000000−4i4i00−2222000002i2−2i200000000000000000000000000
χ474-44-4000-44022−2222−2200004i−4i0000−22220002i2−2i20000000000000000000000000000
χ484-44-4000-44022−2222−220000−4i4i0000−2222000−2i22i20000000000000000000000000000
χ494-44-4000-440−2222−222200004i−4i000022−22000−2i22i20000000000000000000000000000
χ504-44-4000-440−2222−22220000−4i4i000022−220002i2−2i20000000000000000000000000000
χ514-4-444i−4i000022−22−2222000000002i2−2i2000000000ζ−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−ζ7000000000000000000
χ524-4-444i−4i000022−22−2222000000002i2−2i2000000000−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+ζ7000000000000000000
χ534-4-444i−4i0000−222222−2200000000−2i22i2000000000ζ+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−ζ7000000000000000000
χ544-4-444i−4i0000−222222−2200000000−2i22i2000000000−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+ζ7000000000000000000
χ554-4-44−4i4i000022−22−222200000000−2i22i2000000000ζ−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+ζ7000000000000000000
χ564-4-44−4i4i000022−22−222200000000−2i22i2000000000−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−ζ7000000000000000000
χ574-4-44−4i4i0000−222222−22000000002i2−2i2000000000ζ+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+ζ7000000000000000000
χ584-4-44−4i4i0000−222222−22000000002i2−2i2000000000−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−ζ7000000000000000000
χ5988-8-800-80080000000000000000000000000000000000000000000000000

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