Finite Group Databasebeta

← Group #489642

Character table — Group #489642

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444444444444444448888161616161616161616161616161632323232
order1222444444888824448888881616161616161616161616161616161644442444444488161616164488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-111
χ91111-1-111111111-1-11-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-111-1-1-11-111-1-11-11-1
χ101111-1-111111111-1-11-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-11-1-11111-111-1-1-11-11
χ111111-1-111111111-1-11-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-11-1-111-111-1
χ121111-1-111111111-1-11-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-11-1-1111-1-11
χ131111-1-111111111-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-111-111-1-1-11-1-1-111-11-11
χ141111-1-111111111-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-11-1-11111-1-1-1111-11-1
χ151111-1-111111111-1-11-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1111-1-11-1-11
χ161111-1-111111111-1-11-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1111-1-1-111-1
χ172222222222-2-2-2-22222-2-2-2-2-2-20000000000000000222200000000-2-200000000
χ182222222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2-2-2-2000000002200000000
χ192222222-2-222222-2-2-22-2-222-2-2000000000000000000002-2200-2000000000000
χ202222222-2-222222-2-2-22-2-222-2-200000000000000000000-22-2002000000000000
χ212222222-2-22-2-2-2-2-2-2-2222-2-222000000000000000000000002-202-20000000000
χ222222222-2-22-2-2-2-2-2-2-2222-2-22200000000000000000000000-220-220000000000
χ23222222-222-200002-2-2-20000002222−2−2−2−22222−2−2−2−22-2-2200000000002−22−20000
χ24222222-222-200002-2-2-20000002222−2−2−2−22222−2−2−2−2-222-20000000000−22−220000
χ25222222-222-200002-2-2-2000000−2−2−2−22222−2−2−2−222222-2-220000000000−22−220000
χ26222222-222-200002-2-2-2000000−2−2−2−22222−2−2−2−22222-222-200000000002−22−20000
χ272222-2-22222-2-2-2-2-2-22-22222-2-200000000000000002-22-200000000-2200000000
χ282222-2-22222-2-2-2-2-2-22-22222-2-20000000000000000-22-22000000002-200000000
χ292222-2-22-2-22222222-2-222-2-2-2-2000000000000000000002-2-2002000000000000
χ302222-2-22-2-22222222-2-222-2-2-2-200000000000000000000-22200-2000000000000
χ312222-2-22-2-22-2-2-2-222-2-2-2-22222000000000000000000000002-20-220000000000
χ322222-2-22-2-22-2-2-2-222-2-2-2-2222200000000000000000000000-2202-20000000000
χ332222-2-2-222-20000-22-220000002222−2−2−2−2−2−2−2−2222222-2-200000000002−2−220000
χ342222-2-2-222-20000-22-220000002222−2−2−2−2−2−2−2−22222-2-2220000000000−222−20000
χ352222-2-2-222-20000-22-22000000−2−2−2−222222222−2−2−2−222-2-20000000000−222−20000
χ362222-2-2-222-20000-22-22000000−2−2−2−222222222−2−2−2−2-2-22200000000002−2−220000
χ37444444-4-4-4-40000-444-400000000000000000000000000000000000000000000
χ384444-4-4-4-4-4-400004-44400000000000000000000000000000000000000000000
χ3944-4-40004-4022−2222−220000000022−22000000002ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ50000000000000000000000
χ4044-4-40004-4022−2222−220000000022−2200000000−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ50000000000000000000000
χ4144-4-40004-40−2222−222200000000−2222000000002ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ5−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ70000000000000000000000
χ4244-4-40004-40−2222−222200000000−222200000000−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ52ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ70000000000000000000000
χ4344-4-4000-44022−2222−2200000000−22222ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ7000000000000000000000000000000
χ4444-4-4000-44022−2222−2200000000−2222−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ7000000000000000000000000000000
χ4544-4-4000-440−2222−22220000000022−222ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ7−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5000000000000000000000000000000
χ4644-4-4000-440−2222−22220000000022−22−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ72ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ474-44-400400-444-4-4000000000022−2222−2222−2222−22000000000000000000000000000000
χ484-44-400400-444-4-40000000000−2222−2222−2222−2222000000000000000000000000000000
χ494-44-400400-4-4-4440000000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000
χ504-44-400400-4-4-444000000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000
χ514-44-400-4004000000004i−4i00002-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ524-44-400-4004000000004i−4i0000-22-222-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ534-44-400-400400000000−4i4i00002-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ544-44-400-400400000000−4i4i0000-22-222-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ554-4-444i−4i000022−22−22220000002i2−2i200ζ−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−ζ7ζ−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+ζ70000000000000000000000
χ564-4-444i−4i000022−22−22220000002i2−2i200−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+ζ7−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−ζ70000000000000000000000
χ574-4-444i−4i0000−222222−22000000−2i22i200ζ+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+ζ7−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+ζ70000000000000000000000
χ584-4-444i−4i0000−222222−22000000−2i22i200−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−ζ7ζ+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−ζ70000000000000000000000
χ594-4-44−4i4i000022−22−2222000000−2i22i200ζ−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−ζ7−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−ζ70000000000000000000000
χ604-4-44−4i4i000022−22−2222000000−2i22i200−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+ζ7ζ−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+ζ70000000000000000000000
χ614-4-44−4i4i0000−222222−220000002i2−2i200ζ+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+ζ7ζ+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−ζ70000000000000000000000
χ624-4-44−4i4i0000−222222−220000002i2−2i200−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−ζ7−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+ζ70000000000000000000000

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