Finite Group Databasebeta

← Group #145187

Character table — Group #145187

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order1222224444444488884488888816161616161616161616161616161616444444888888161616168888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-111-111-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ922222222222222-2-2-2-222-2-2-2-2-2-20000000000000000200200-2-2000000000000
χ1022222222222222-2-2-2-222-2-2-2-2-2-20000000000000000-200-20022000000000000
χ11222222222-2-2-22-20000-2-200000022222222−2−2−2−2−2−2−2−20000002i−2i0000i2i2−i2−i20000
χ12222222222-2-2-22-20000-2-200000022222222−2−2−2−2−2−2−2−2000000−2i2i0000−i2−i2i2i20000
χ13222222222-2-2-22-20000-2-2000000−2−2−2−2−2−2−2−2222222220000002i−2i0000−i2−i2i2i20000
χ14222222222-2-2-22-20000-2-2000000−2−2−2−2−2−2−2−222222222000000−2i2i0000i2i2−i2−i20000
χ15222222-2-2-2222-222222-2-222-2-2-2-200000000000000000220-2-200000000000000
χ16222222-2-2-2222-222222-2-222-2-2-2-200000000000000000-2-202200000000000000
χ17222222-2-2-2222-22-2-2-2-2-2-2-2-22222000000000000000000000000000000002-200
χ18222222-2-2-2222-22-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2200
χ192222-2-222-2-222-2-222222-2-2-222-2-20000000000000000000000002i2i−2i−2i00000000
χ202222-2-222-2-222-2-222222-2-2-222-2-2000000000000000000000000−2i−2i2i2i00000000
χ212222-2-222-2-222-2-2-2-2-2-22-222-2-22200000000000000000000000000000000002i−2i
χ222222-2-222-2-222-2-2-2-2-2-22-222-2-2220000000000000000000000000000000000−2i2i
χ232222-2-2-2-222-2-22200002-20000002222−2−2−2−22222−2−2−2−2200-2000000002−22−20000
χ242222-2-2-2-222-2-22200002-20000002222−2−2−2−22222−2−2−2−2-200200000000−22−220000
χ252222-2-2-2-222-2-22200002-2000000−2−2−2−22222−2−2−2−22222200-200000000−22−220000
χ262222-2-2-2-222-2-22200002-2000000−2−2−2−22222−2−2−2−22222-2002000000002−22−20000
χ272222-2-2-2-22-2222-22222-22-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000
χ282222-2-2-2-22-2222-22222-22-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000
χ292222-2-2-2-22-2222-2-2-2-2-2-222222-2-200000000000000000000000000002i−2i−2i2i0000
χ302222-2-2-2-22-2222-2-2-2-2-2-222222-2-20000000000000000000000000000−2i2i2i−2i0000
χ312-22-22-200022-20-222-2-2002-2000022−2−222−2−222−2−222−2−202-2000002−22−200000000
χ322-22-22-200022-20-222-2-2002-2000022−2−222−2−222−2−222−2−20-2200000−22−2200000000
χ332-22-22-200022-20-222-2-2002-20000−2−222−2−222−2−222−2−22202-200000−22−2200000000
χ342-22-22-200022-20-222-2-2002-20000−2−222−2−222−2−222−2−2220-22000002−22−200000000
χ352-22-2-22000-22-20222-2-200-22000022−2−2−2−222−2−22222−2−200002i−2i00i2−i2−i2i200000000
χ362-22-2-22000-22-20222-2-200-22000022−2−2−2−222−2−22222−2−20000−2i2i00−i2i2i2−i200000000
χ372-22-2-22000-22-20222-2-200-220000−2−22222−2−222−2−2−2−22200002i−2i00−i2i2i2−i200000000
χ382-22-2-22000-22-20222-2-200-220000−2−22222−2−222−2−2−2−2220000−2i2i00i2−i2−i2i200000000
χ39444444-4-4-4-4-4-4-4-4000044000000000000000000000000000000000000000000
χ404444-4-444-44-4-4-440000-44000000000000000000000000000000000000000000
χ4144-4-400004000-4022−2222−2200000022−2200002ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ4244-4-400004000-4022−2222−2200000022−220000−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ4344-4-400004000-40−2222−2222000000−222200002ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ4444-4-400004000-40−2222−2222000000−22220000−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ4544-4-40000-40004022−2222−22000000−22222ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5000000002ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000
χ4644-4-40000-40004022−2222−22000000−2222−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ500000000−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000
χ4744-4-40000-400040−2222−222200000022−222ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ700000000−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000
χ4844-4-40000-400040−2222−222200000022−22−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7000000002ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000
χ494-44-44-400044-40-4-4-44400-440000000000000000000000000000000000000000
χ504-44-44-4000-4-440400000000000022-2-222-2-2-2-222-2-22200000000000000000000
χ514-44-44-4000-4-4404000000000000-2-222-2-22222-2-222-2-200000000000000000000
χ524-44-4-440004-440-400000000000022-2-2-2-22222-2-2-2-22200000000000000000000
χ534-44-4-440004-440-4000000000000-2-22222-2-2-2-22222-2-200000000000000000000
χ544-44-4-44000-44-404-4-444004-40000000000000000000000000000000000000000
χ554-4-44004i−4i00000022−22−222200002i2−2i200ζ+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−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ564-4-44004i−4i00000022−22−222200002i2−2i200−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+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ574-4-44004i−4i000000−222222−220000−2i22i200ζ−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+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+ζ700000000000000000000
χ584-4-44004i−4i000000−222222−220000−2i22i200−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−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−ζ700000000000000000000
χ594-4-4400−4i4i00000022−22−22220000−2i22i200ζ+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+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ604-4-4400−4i4i00000022−22−22220000−2i22i200−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−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ614-4-4400−4i4i000000−222222−2200002i2−2i200ζ−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−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+ζ700000000000000000000
χ624-4-4400−4i4i000000−222222−2200002i2−2i200−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+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−ζ700000000000000000000

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