Finite Group Databasebeta

← Group #142107

Character table — Group #142107

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222244444444888888888888444444444488888888881616161616161616161616161616161616161616161616164444
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
χ511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ9111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ14111111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ15111111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ16111111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222222-2-22222-2-222-2-2-2-2-2-2-2-222-2-2-2-222-2-20000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000
χ19222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2-2220000000000000000000000000000
χ20222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2222222-2-20000000000000000000000000000
χ212222-2-2222222-2-2222200222200-2-200000000-2-20000-2-20000000000000000002−22−22−22−20000
χ222222-2-2222222-2-2222200222200-2-200000000-2-20000-2-2000000000000000000−22−22−22−220000
χ232222-2-2222222-2-2-2-2-2-200-2-2-2-200-2-20000000022000022000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ242222-2-2222222-2-2-2-2-2-200-2-2-2-200-2-20000000022000022000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ252222-2-222-2-2-2-2220000220000222-2000000000022-2-200-2-222−2−222−2−222−2−222−2−2000000000000
χ262222-2-222-2-2-2-2220000220000222-2000000000022-2-200-2-2−2−222−2−222−2−222−2−222000000000000
χ272222-2-222-2-2-2-2220000-2-20000-2-22-20000000000-2-2220022i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ282222-2-222-2-2-2-2220000-2-20000-2-22-20000000000-2-2220022−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ292222-2-2-2-222-2-222000022000022-220000000000-2-22200-2-222−2−2−2−222−2−22222−2−2000000000000
χ302222-2-2-2-222-2-222000022000022-220000000000-2-22200-2-2−2−22222−2−222−2−2−2−222000000000000
χ312222-2-2-2-222-2-2220000-2-20000-2-2-22000000000022-2-20022i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ322222-2-2-2-222-2-2220000-2-20000-2-2-22000000000022-2-20022−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ332222-2-2-2-2-2-222-2-2222200-2-2-2-2002200000000-2-2000022000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ342222-2-2-2-2-2-222-2-2222200-2-2-2-2002200000000-2-2000022000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ352222-2-2-2-2-2-222-2-2-2-2-2-2002222002200000000220000-2-20000000000000000002−2−22−222−20000
χ362222-2-2-2-2-2-222-2-2-2-2-2-2002222002200000000220000-2-2000000000000000000−222−22−2−220000
χ3722-2-22-200002-22-200002222-2-2-2-20022-2-200000000002-22-200002-22-22-22-20000000000000000
χ3822-2-22-200002-22-200002222-2-2-2-20022-2-200000000002-22-20000-22-22-22-220000000000000000
χ3922-2-22-200002-22-2000022-2-222-2-200-2-2220000000000-222-22-22-2000000002-22-2000000000000
χ4022-2-22-200002-22-2000022-2-222-2-200-2-2220000000000-222-2-22-2200000000-22-22000000000000
χ4122-2-22-200002-22-20000-2-222-2-22200-2-22200000000002-2-222i−2i2i−2i00000000−2i2i−2i2i000000000000
χ4222-2-22-200002-22-20000-2-222-2-22200-2-22200000000002-2-22−2i2i−2i2i000000002i−2i2i−2i000000000000
χ4322-2-22-200002-22-20000-2-2-2-222220022-2-20000000000-22-2200002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4422-2-22-200002-22-20000-2-2-2-222220022-2-20000000000-22-220000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4522-2-2-220000-222-222-2-2220000-2-200000022-2-22-2000000-222−2−222−2−222−2−222−2−22000000000000
χ4622-2-2-220000-222-222-2-2220000-2-200000022-2-22-2000000-22−222−2−222−2−222−2−222−2000000000000
χ4722-2-2-220000-222-222-2-2-2-2000022000000-2-2222-20000002-2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ4822-2-2-220000-222-222-2-2-2-2000022000000-2-2222-20000002-2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ4922-2-2-220000-222-2-2-222220000-2-2000000-2-222-22000000-222−2−22−222−2−222−22−2−22000000000000
χ5022-2-2-220000-222-2-2-222220000-2-2000000-2-222-22000000-22−222−22−2−222−2−22−222−2000000000000
χ5122-2-2-220000-222-2-2-222-2-200002200000022-2-2-220000002-2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ5222-2-2-220000-222-2-2-222-2-200002200000022-2-2-220000002-2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4000000000000-440000000000000000000000000000000000000000000000
χ54444444-4-444-4-4-4-40000000000004-40000000000000000000000000000000000000000000000
χ5544-4-44-40000-44-4444-4-4000000000000000000-44000000000000000000000000000000000000
χ5644-4-44-40000-44-44-4-4440000000000000000004-4000000000000000000000000000000000000
χ5744-4-4-4400004-4-4400000044-4-4000000000000000000-44000000000000000000000000000000
χ5844-4-4-4400004-4-44000000-4-4440000000000000000004-4000000000000000000000000000000
χ594-44-400004-400002i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i2002-22-22-22-200002i2−2i200000000000000000000000000000000
χ604-44-400004-400002i2−2i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i200-22-22-22-220000−2i22i200000000000000000000000000000000
χ614-44-400004-40000−2i22i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i200-22-22-22-2200002i2−2i200000000000000000000000000000000
χ624-44-400004-40000−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2002-22-22-22-20000−2i22i200000000000000000000000000000000
χ634-44-40000-4400002i2−2i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i200-22-222-22-20000−2i22i200000000000000000000000000000000
χ644-44-40000-4400002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i2002-22-2-22-2200002i2−2i200000000000000000000000000000000
χ654-44-40000-440000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2002-22-2-22-220000−2i22i200000000000000000000000000000000
χ664-44-40000-440000−2i22i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i200-22-222-22-200002i2−2i200000000000000000000000000000000
χ674-4-44004-40000002i2−2i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i2002-2-222-2-22002i2−2i20000000000000000000000000000000000
χ684-4-44004-40000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i200-222-2-222-200−2i22i20000000000000000000000000000000000
χ694-4-44004-4000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i200-222-2-222-2002i2−2i20000000000000000000000000000000000
χ704-4-44004-4000000−2i22i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2002-2-222-2-2200−2i22i20000000000000000000000000000000000
χ714-4-4400-440000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i200-222-22-2-2200−2i22i20000000000000000000000000000000000
χ724-4-4400-440000002i2−2i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i2002-2-22-222-2002i2−2i20000000000000000000000000000000000
χ734-4-4400-44000000−2i22i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i2002-2-22-222-200−2i22i20000000000000000000000000000000000
χ744-4-4400-44000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i200-222-22-2-22002i2−2i20000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).