Finite Group Databasebeta

← Group #138486

Character table — Group #138486

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444444442244448888888844888816161616161616161616161616161616888888884444
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
χ511111111111111-1-11-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-11-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111-1-1-1-1-111-1-1-1111-11111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ14111111-1-1-1-1-111-1-1-1111-11111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ15111111-1-1-1-1-111-1-1-1111-11111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ16111111-1-1-1-1-111-1-1-1111-11111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222222-2-22-2-22-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222222-2-2-2-2222-222-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ20222222222-2-2-2-2222-222-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ21222222222-2-2-2-22-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−222000000000000
χ22222222222-2-2-2-22-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−2000000000000
χ23222222-2-2-222-2-2-222-2-2-2200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ24222222-2-2-222-2-2-222-2-2-2200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ25222222-2-2-222-2-2-2-2-2-2222000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ26222222-2-2-222-2-2-2-2-2-2222000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ27222222-2-2-2-2-222-2222-2-2-2-2-2-2-222222-2-2-2220000000000000000000000000000
χ28222222-2-2-2-2-222-2-2-2222-2-2-2-2-22222-2222-2-20000000000000000000000000000
χ292222-2-222-22222-200-200-222-2-222-2-2000000000000000000000000002i−2i2i−2i0000
χ302222-2-222-22222-200-200-222-2-222-2-200000000000000000000000000−2i2i−2i2i0000
χ312222-2-222-22222-200-200-2-2-222-2-22200000000000000000000002i−2i2i−2i00000000
χ322222-2-222-22222-200-200-2-2-222-2-2220000000000000000000000−2i2i−2i2i00000000
χ332222-2-2-2-22-2-222200-200222-2-2-2-222000000000000000000000000002-2-220000
χ342222-2-2-2-22-2-222200-200222-2-2-2-22200000000000000000000000000-222-20000
χ352222-2-2-2-22-2-222200-2002-2-22222-2-200000000000000000000002-2-2200000000
χ362222-2-2-2-22-2-222200-2002-2-22222-2-20000000000000000000000-222-200000000
χ3722-2-22-22-220000-22-202-202−22−22−22−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3822-2-22-22-220000-22-202-202−22−22−22−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3922-2-22-22-220000-22-202-20−22−22−22−2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ4022-2-22-22-220000-22-202-20−22−22−22−2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ4122-2-22-22-220000-2-220-2202−22−22−22−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4222-2-22-22-220000-2-220-2202−22−22−22−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4322-2-22-22-220000-2-220-220−22−22−22−22002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ4422-2-22-22-220000-2-220-220−22−22−22−22002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ4522-2-22-2-22-2000022-20-2202−22−2−22−22002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4622-2-22-2-22-2000022-20-2202−22−2−22−22002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4722-2-22-2-22-2000022-20-220−22−222−22−200−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4822-2-22-2-22-2000022-20-220−22−222−22−200−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4922-2-22-2-22-200002-2202-202−22−2−22−2200−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ5022-2-22-2-22-200002-2202-202−22−2−22−2200−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ5122-2-22-2-22-200002-2202-20−22−222−22−2002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ5222-2-22-2-22-200002-2202-20−22−222−22−2002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ534444-4-444-4-4-4-4-4-4004004000000000000000000000000000000000000000000
χ544444-4-4-4-4444-4-4400400-4000000000000000000000000000000000000000000
χ5544-4-4-444-4-40000400000022−22−222222−22−22220000000000000000000000000000000000
χ5644-4-4-444-4-400004000000−222222−22−222222−220000000000000000000000000000000000
χ5744-4-4-44-4440000-400000022−22−2222−222222−220000000000000000000000000000000000
χ5844-4-4-44-4440000-4000000−222222−2222−22−22220000000000000000000000000000000000
χ598-88-800000008-80000000000000000000000000000000000000000000000000
χ608-88-80000000-880000000000000000000000000000000000000000000000000
χ618-8-88000008-8000000000000000000000000000000000000000000000000000
χ628-8-8800000-88000000000000000000000000000000000000000000000000000

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