Finite Group Databasebeta

← Group #488604

Character table — Group #488604

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444444444444448888888824888816161616161616161616161616161616224444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-11-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-1
χ10111111-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-11-11
χ11111111-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1111-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-11-11
χ12111111-1-1-1-1-1-111-1111-1-1-1-1-1-11111-1111-1-1-1-1-1-11111-1-1-1-11111-11-11-11-111-11-1
χ13111111-1-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-11-111-1-11
χ14111111-1-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-11-111-11-1-111-1
χ15111111-1-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-11-11-1-11-11-111-1
χ16111111-1-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-11-111-11-11-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ18222222222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-2-2-222-22200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-2-222-22200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−222000000000000
χ222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−2000000000000
χ23222222-2-2-2-222-2-2222-2-2-2000000002-2000022−2−2−2−22222−2−2−2−222000000000000
χ24222222-2-2-2-222-2-2222-2-2-2000000002-20000−2−22222−2−2−2−22222−2−2000000000000
χ25222222-2-2-2-222-2-22-2-2-22200000000-22000022−2−2−2−222−2−22222−2−2000000000000
χ26222222-2-2-2-222-2-22-2-2-22200000000-220000−2−22222−2−222−2−2−2−222000000000000
χ27222222-2-2-2-2-2-222-2222-2-22222-2-2-2-2-22-2-2220000000000000000000000000000
χ28222222-2-2-2-2-2-222-2-2-22222222-2-2-2-22-222-2-20000000000000000000000000000
χ292222-2-222-2-22222-200-20022-2-222-2-2000000000000000000000022-2-200000000
χ302222-2-222-2-22222-200-20022-2-222-2-20000000000000000000000-2-22200000000
χ312222-2-222-2-22222-200-200-2-222-2-2220000000000000000000000000022-2-20000
χ322222-2-222-2-22222-200-200-2-222-2-22200000000000000000000000000-2-2220000
χ332222-2-2-2-222-2-222200-20022-2-2-2-222000000000000000000000000002-2-220000
χ342222-2-2-2-222-2-222200-20022-2-2-2-22200000000000000000000000000-222-20000
χ352222-2-2-2-222-2-222200-200-2-22222-2-200000000000000000000002-2-2200000000
χ362222-2-2-2-222-2-222200-200-2-22222-2-20000000000000000000000-222-200000000
χ3722-2-2-222-22-2000002i−2i02i−2i2−22−22−22−200i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3822-2-2-222-22-2000002i−2i02i−2i2−22−22−22−200i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3922-2-2-222-22-2000002i−2i02i−2i−22−22−22−2200−i2i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4022-2-2-222-22-2000002i−2i02i−2i−22−22−22−2200−i2i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4122-2-2-222-22-200000−2i2i0−2i2i2−22−22−22−200−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4222-2-2-222-22-200000−2i2i0−2i2i2−22−22−22−200−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4322-2-2-222-22-200000−2i2i0−2i2i−22−22−22−2200i2−i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4422-2-2-222-22-200000−2i2i0−2i2i−22−22−22−2200i2−i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4522-2-2-22-22-22000002i−2i0−2i2i2−22−2−22−2200−i2i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4622-2-2-22-22-22000002i−2i0−2i2i2−22−2−22−2200−i2i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4722-2-2-22-22-22000002i−2i0−2i2i−22−222−22−200i2−i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4822-2-2-22-22-22000002i−2i0−2i2i−22−222−22−200i2−i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4922-2-2-22-22-2200000−2i2i02i−2i2−22−2−22−2200i2−i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ5022-2-2-22-22-2200000−2i2i02i−2i2−22−2−22−2200i2−i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ5122-2-2-22-22-2200000−2i2i02i−2i−22−222−22−200−i2i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ5222-2-2-22-22-2200000−2i2i02i−2i−22−222−22−200−i2i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ534444-4-444-4-4-4-4-4-4400400000000000000000000000000000000000000000000
χ544444-4-4-4-44444-4-4-400400000000000000000000000000000000000000000000
χ5544-4-44-44-4-44000000000022−22−222222−22−22220000000000000000000000000000000000
χ5644-4-44-44-4-440000000000−222222−22−222222−220000000000000000000000000000000000
χ5744-4-44-4-444-4000000000022−22−2222−222222−220000000000000000000000000000000000
χ5844-4-44-4-444-40000000000−222222−2222−22−22220000000000000000000000000000000000
χ598-88-80000008-800000000000000000000000000000000000000000000000000
χ608-88-8000000-8800000000000000000000000000000000000000000000000000
χ618-8-88000000008-8000000000000000000000000000000000000000000000000
χ628-8-8800000000-88000000000000000000000000000000000000000000000000

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