Finite Group Databasebeta

← Group #138207

Character table — Group #138207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order12222244444488884448888244488888161616161616161688888888161616162488
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9111111111-1-11-1-1-1-1-1-1-111-1-11-1-11111-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i1-11-1
χ10111111111-1-11-1-1-1-1-1-1-111-1-11-1-11111-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i-11-11
χ11111111111-1-11-1-1-1-1-1-1-111-1-11-1-11111-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iii-11-11
χ12111111111-1-11-1-1-1-1-1-1-111-1-11-1-11111-1-1−i−i−i−iiiii−i−iii−i−iii−i−iii1-11-1
χ13111111111-1-11-1-1-1-1-1-1-111-1-1-111-11-1-111iiii−i−i−i−iii−i−i−i−iii−i−iii1-1-11
χ14111111111-1-11-1-1-1-1-1-1-111-1-1-111-11-1-111iiii−i−i−i−i−i−iiiii−i−i−i−iii-111-1
χ15111111111-1-11-1-1-1-1-1-1-111-1-1-111-11-1-111−i−i−i−iiiiiii−i−i−i−iiiii−i−i-111-1
χ16111111111-1-11-1-1-1-1-1-1-111-1-1-111-11-1-111−i−i−i−iiiii−i−iiiii−i−iii−i−i1-1-11
χ17222222222222-2-2-2-2222-2-2-2-22222-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222-2-222222-2-2-2-2-2222-2-22-2-2-222000000000000000000000000
χ20222222222-2-222222-2-2-2-2-222-222-2-222-2-2000000000000000000000000
χ212222-2-22-2-222200002-2-2000022-2-20000022−2−222−2−2000000002−22−20000
χ222222-2-22-2-222200002-2-2000022-2-200000−2−222−2−22200000000−22−220000
χ232222-2-22-2-222200002-2-20000-2-2220000022−2−222−2−200000000−22−220000
χ242222-2-22-2-222200002-2-20000-2-22200000−2−222−2−222000000002−22−20000
χ252222-2-22-2-2-2-220000-22200002-22-200000i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i20000
χ262222-2-22-2-2-2-220000-22200002-22-200000−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i20000
χ272222-2-22-2-2-2-220000-2220000-22-2200000i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i20000
χ282222-2-22-2-2-2-220000-2220000-22-2200000−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i20000
χ292222-2-2-22222-22222-22-222-2-20000-200000000000000002-22-200000000
χ302222-2-2-22222-22222-22-222-2-20000-20000000000000000-22-2200000000
χ312222-2-2-22222-2-2-2-2-2-22-2-2-222000020000000000002-22-2000000000000
χ322222-2-2-22222-2-2-2-2-2-22-2-2-22200002000000000000-22-22000000000000
χ332222-2-2-222-2-2-222222-22-2-2-2-2000020000000000002i−2i−2i2i000000000000
χ342222-2-2-222-2-2-222222-22-2-2-2-200002000000000000−2i2i2i−2i000000000000
χ352222-2-2-222-2-2-2-2-2-2-22-2222220000-200000000000000002i−2i−2i2i00000000
χ362222-2-2-222-2-2-2-2-2-2-22-2222220000-20000000000000000−2i2i2i−2i00000000
χ37444444-4-4-444-40000-4-440000000000000000000000000000000000000
χ38444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000
χ3944-4-4000004i−4i02i2−2i22i2−2i200022−2200000000000ζ+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−ζ70000000000000000
χ4044-4-4000004i−4i02i2−2i22i2−2i200022−2200000000000−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+ζ70000000000000000
χ4144-4-4000004i−4i0−2i22i2−2i22i2000−222200000000000ζ+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+ζ70000000000000000
χ4244-4-4000004i−4i0−2i22i2−2i22i2000−222200000000000−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−ζ70000000000000000
χ4344-4-400000−4i4i02i2−2i22i2−2i2000−222200000000000ζ−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−ζ70000000000000000
χ4444-4-400000−4i4i02i2−2i22i2−2i2000−222200000000000−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+ζ70000000000000000
χ4544-4-400000−4i4i0−2i22i2−2i22i200022−2200000000000ζ−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+ζ70000000000000000
χ4644-4-400000−4i4i0−2i22i2−2i22i200022−2200000000000−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−ζ70000000000000000
χ474-4-444-444-400-40000000000000000004i−4i000000000000000000000000
χ484-4-444-444-400-4000000000000000000−4i4i000000000000000000000000
χ494-4-444-4-4-4400444-4-400000-44000000000000000000000000000000000
χ504-4-444-4-4-44004-4-444000004-4000000000000000000000000000000000
χ514-4-44-444-4400-444-4-4000004-4000000000000000000000000000000000
χ524-4-44-444-4400-4-4-44400000-44000000000000000000000000000000000
χ534-4-44-44-44-400400000000000000004-400000000000000000000000000
χ544-4-44-44-44-40040000000000000000-4400000000000000000000000000
χ558-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000
χ568-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000

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