Finite Group Databasebeta

← Group #138191

Character table — Group #138191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888224444444488888888888816161616161616161616161616161616888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111111-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111111-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111111-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-222-22222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ202222222222-2-2-222-222222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2122222222-2-2222-2-220000000022-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−2000000000000
χ2222222222-2-2222-2-220000000022-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−222000000000000
χ2322222222-2-2222-2-2200000000-2-2-2-22222-2-200000000000022−2−222−2−2−2−222−2−222000000000000
χ2422222222-2-2222-2-2200000000-2-2-2-22222-2-2000000000000−2−222−2−22222−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2922-2-2-2-2220022-200-222−2−222−2−22-20000002-222−2−222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3022-2-2-2-2220022-200-222−2−222−2−22-20000002-222−2−222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3122-2-2-2-2220022-200-222−2−222−2−2-22000000-2222−2−2−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3222-2-2-2-2220022-200-222−2−222−2−2-22000000-2222−2−2−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3322-2-2-2-2220022-200-2−2−222−2−2222-20000002-2−2−222−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ3422-2-2-2-2220022-200-2−2−222−2−2222-20000002-2−2−222−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ3522-2-2-2-2220022-200-2−2−222−2−222-22000000-22−2−22222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ3622-2-2-2-2220022-200-2−2−222−2−222-22000000-22−2−22222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ3722-2-2-2-22200-2-2200222−2−222−2−22-2000000-22−2−222−2−22222−2−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3822-2-2-2-22200-2-2200222−2−222−2−22-2000000-22−2−222−2−22222−2−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3922-2-2-2-22200-2-2200222−2−222−2−2-220000002-2−2−22222−2−2−2−222ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4022-2-2-2-22200-2-2200222−2−222−2−2-220000002-2−2−22222−2−2−2−222−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4122-2-2-2-22200-2-22002−2−222−2−2222-2000000-2222−2−222−2−2−2−222ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4222-2-2-2-22200-2-22002−2−222−2−2222-2000000-2222−2−222−2−2−2−222−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4322-2-2-2-22200-2-22002−2−222−2−222-220000002-222−2−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4422-2-2-2-22200-2-22002−2−222−2−222-220000002-222−2−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ452-2-2-222-22-2-22-2222-22-22-22-22-2002-20000002-22-20000000000000000000000002i−2i2i−2i00000000
χ462-2-2-222-22-2-22-2222-22-22-22-22-2002-20000002-22-2000000000000000000000000−2i2i−2i2i00000000
χ472-2-2-222-22-2-22-2222-2-22-22-22-22002-2000000-22-2200000000000000000000000000002i−2i2i−2i0000
χ482-2-2-222-22-2-22-2222-2-22-22-22-22002-2000000-22-220000000000000000000000000000−2i2i−2i2i0000
χ492-2-2-222-22-2-2-22-22222-22-22-22-200-22000000-22-2200000000000000000000000000002-2-220000
χ502-2-2-222-22-2-2-22-22222-22-22-22-200-22000000-22-220000000000000000000000000000-222-20000
χ512-2-2-222-22-2-2-22-2222-22-22-22-2200-220000002-22-20000000000000000000000002-2-2200000000
χ522-2-2-222-22-2-2-22-2222-22-22-22-2200-220000002-22-2000000000000000000000000-222-200000000
χ53444-44-4-4-40000000022−22−2222−222222−220000004-400000022−2222−2200000000000000000000000000000000
χ54444-44-4-4-40000000022−22−2222−222222−22000000-44000000−2222−222200000000000000000000000000000000
χ55444-44-4-4-400000000−222222−2222−22−22220000004-4000000−2222−222200000000000000000000000000000000
χ56444-44-4-4-400000000−222222−2222−22−2222000000-4400000022−2222−2200000000000000000000000000000000
χ5744-44-44-4-44-40004-4000000000000000000000004-4-4400000000000000000000000000000000
χ5844-44-44-4-44-40004-400000000000000000000000-444-400000000000000000000000000000000
χ5944-44-44-4-4-44000-4404-44-4-44-4400000000000000000000000000000000000000000000000000
χ6044-44-44-4-4-44000-440-44-444-44-400000000000000000000000000000000000000000000000000
χ614-444-4-4-44004-4-400422−22−222222−22−2222000000000022−22−2222000000000000000000000000000000000000
χ624-444-4-4-44004-4-4004−222222−22−222222−220000000000−222222−22000000000000000000000000000000000000
χ634-444-4-4-4400-44400-422−22−222222−22−22220000000000−222222−22000000000000000000000000000000000000
χ644-444-4-4-4400-44400-4−222222−22−222222−22000000000022−22−2222000000000000000000000000000000000000
χ654-44-4-444-44-4000-4404444-4-4-4-400000000000000000000000000000000000000000000000000
χ664-44-4-444-44-4000-440-4-4-4-4444400000000000000000000000000000000000000000000000000
χ674-44-4-444-4-440004-40000000000000000000000000004i−4i4i−4i0000000000000000000000000000
χ684-44-4-444-4-440004-4000000000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ694-4-444-44-4000000002222−22−22−22−22222200004i−4i0000000000002i2−2i2−2i22i20000000000000000000000000000
χ704-4-444-44-4000000002222−22−22−22−2222220000−4i4i000000000000−2i22i22i2−2i20000000000000000000000000000
χ714-4-444-44-400000000−22−2222222222−22−2200004i−4i000000000000−2i22i22i2−2i20000000000000000000000000000
χ724-4-444-44-400000000−22−2222222222−22−220000−4i4i0000000000002i2−2i2−2i22i20000000000000000000000000000
χ734-4-4-444-44444-44-4-4-40000000000-440000000000000000000000000000000000000000000000
χ744-4-4-444-4444-44-4-4-4400000000004-40000000000000000000000000000000000000000000000

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