Finite Group Databasebeta

← Group #140458

Character table — Group #140458

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888448888888888888888888816161616161616161616161616161616444488884444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−i
χ131111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ141111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ151111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−i
χ161111-1-1-1-1-1-1-11111-111-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-222-2-2-222222222-2-2-2-2-2-2000000000000000000000000000000002-22-200000000
χ202222222222-222-2-2-222222222-2-2-2-2-2-200000000000000000000000000000000-22-2200000000
χ212222222222-222-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i2i−2i0000
χ222222222222-222-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-22-2-222200000000-2-2000022-2-222-2-20000000022−2−222−2−222−2−222−2−2000000000000
χ2422222222-2-22-2-222200000000-2-2000022-2-222-2-200000000−2−222−2−222−2−222−2−222000000000000
χ2522222222-2-22-2-222200000000-2-20000-2-222-2-2220000000022−2−222−2−2−2−222−2−222000000000000
χ2622222222-2-22-2-222200000000-2-20000-2-222-2-22200000000−2−222−2−22222−2−222−2−2000000000000
χ272222-2-2-2-222-2-2-222-2000000002-2000022-2-2-2-2220000000022−2−2−2−22222−2−2−2−222000000000000
χ282222-2-2-2-222-2-2-222-2000000002-2000022-2-2-2-22200000000−2−22222−2−2−2−22222−2−2000000000000
χ292222-2-2-2-222-2-2-222-2000000002-20000-2-22222-2-20000000022−2−2−2−222−2−22222−2−2000000000000
χ302222-2-2-2-222-2-2-222-2000000002-20000-2-22222-2-200000000−2−22222−2−222−2−2−2−222000000000000
χ312222-2-2-2-2-2-2222-2-2222-2-2-2-2222-2-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-2-2-2222-2-2222-2-2-2-2222-2-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-2-2-2222-2-22-2-22222-2-22-222-2-20000000000000000000000000000000000002-2-220000
χ342222-2-2-2-2-2-2222-2-22-2-22222-2-22-222-2-2000000000000000000000000000000000000-222-20000
χ352222-2-2-2-2-2-2-22222-2-2-22222-2-2-22-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ362222-2-2-2-2-2-2-22222-2-2-22222-2-2-22-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ3722-2-222-2-200-2002-222−222−2−22−2002−22−2002-2002-222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3822-2-222-2-200-2002-222−222−2−22−2002−22−2002-2002-222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3922-2-222-2-200-2002-222−222−2−22−2002−22−200-2200-22−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4022-2-222-2-200-2002-222−222−2−22−2002−22−200-2200-22−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4122-2-222-2-200-2002-22−22−2−222−2200−22−22002-2002-2−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4222-2-222-2-200-2002-22−22−2−222−2200−22−22002-2002-2−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4322-2-222-2-200-2002-22−22−2−222−2200−22−2200-2200-2222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4422-2-222-2-200-2002-22−22−2−222−2200−22−2200-2200-2222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4522-2-2-2-222002002-2-22−2−2−2222−2002−2−22002-200-2222−2−2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4622-2-2-2-222002002-2-22−2−2−2222−2002−2−22002-200-2222−2−2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4722-2-2-2-222002002-2-22−2−2−2222−2002−2−2200-22002-2−2−22222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4822-2-2-2-222002002-2-22−2−2−2222−2002−2−2200-22002-2−2−22222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4922-2-2-2-222002002-2-2−2222−2−2−2200−222−2002-200-22−2−22222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ5022-2-2-2-222002002-2-2−2222−2−2−2200−222−2002-200-22−2−22222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ5122-2-2-2-222002002-2-2−2222−2−2−2200−222−200-22002-222−2−2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ5222-2-2-2-222002002-2-2−2222−2−2−2200−222−200-22002-222−2−2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ544444-4-4-4-4444-4-4-4-4400000000-44000000000000000000000000000000000000000000000000
χ5544-4-444-4-400400-44-422−222222−22−2222−2200−2222−222200000000000000000000000000000000000000000000
χ5644-4-444-4-400400-44-4−2222−22−222222−22220022−2222−2200000000000000000000000000000000000000000000
χ5744-4-4-4-44400-400-44422−22−22−22222222−2200−222222−2200000000000000000000000000000000000000000000
χ5844-4-4-4-44400-400-444−22222222−22−22−22220022−22−222200000000000000000000000000000000000000000000
χ594-44-44-44-40000000022−2222−2222−22−22220000002i2−2i2002i2−2i2002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ604-44-44-44-40000000022−2222−2222−22−2222000000−2i22i200−2i22i200−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ614-44-44-44-400000000−2222−2222−222222−220000002i2−2i2002i2−2i200−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ624-44-44-44-400000000−2222−2222−222222−22000000−2i22i200−2i22i2002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ634-44-4-44-440000000022−22−2222−2222−22220000002i2−2i200−2i22i2002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ644-44-4-44-440000000022−22−2222−2222−2222000000−2i22i2002i2−2i200−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ654-44-4-44-4400000000−222222−2222−2222−220000002i2−2i200−2i22i200−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ664-44-4-44-4400000000−222222−2222−2222−22000000−2i22i2002i2−2i2002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ674-4-444-4-444-404-400000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ684-4-444-4-444-404-40000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ694-4-444-4-44-440-44000444-4-44-4-400000000000000000000000000000000000000000000000000
χ704-4-444-4-44-440-44000-4-4-444-44400000000000000000000000000000000000000000000000000
χ714-4-44-444-44-40-4400044-444-4-4-400000000000000000000000000000000000000000000000000
χ724-4-44-444-44-40-44000-4-44-4-444400000000000000000000000000000000000000000000000000
χ734-4-44-444-4-4404-400000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ744-4-44-444-4-4404-40000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000

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