Finite Group Databasebeta

← Group #140449

Character table — Group #140449

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222244448888888816161616161616164444888816161616161616161616161644448888161616161616161616161616161616164444
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911-1-11-1-111-1-1-111-1-1111111-1-1-1-111-1-11-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ1011-1-11-1-111-1-1-111-1-1111111-1-1-1-111-1-11-1-1111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ1111-1-11-1-111-1-1-111-1-1111111-1-1-1-111-1-11-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ1211-1-11-1-111-1-1-111-1-1111111-1-1-1-111-1-11-1-1111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-111-1-111i−ii−i
χ1311-1-11-1-111-1-1-111-1-111-1-1-1-1111111-1-11-1-11-1-111-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ1411-1-11-1-111-1-1-111-1-111-1-1-1-1111111-1-11-1-11-1-111-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ1511-1-11-1-111-1-1-111-1-111-1-1-1-1111111-1-11-1-11-1-111-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ1611-1-11-1-111-1-1-111-1-111-1-1-1-1111111-1-11-1-11-1-111-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ17222222222222-2-2-2-22200000000-2-2-2-222-2-20000000000002222-2-2-2-200000000000000000000
χ18222222222222-2-2-2-22200000000-2-2-2-222-2-2000000000000-2-2-2-2222200000000000000000000
χ192222222222-2-22222-2-222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ202222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222220000000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ232222-2-222-2-22200002222−2−222−2−20000-2-2002−22−222−2−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ242222-2-222-2-22200002222−2−222−2−20000-2-2002−22−222−2−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ252222-2-222-2-222000022−2−222−2−2220000-2-200−22−22−2−222−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ262222-2-222-2-222000022−2−222−2−2220000-2-200−22−22−2−222−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ272222-2-222-2-2-2-20000-2-222−2−222−2−2000022002−22−2−2−222−2−2222-22-200002−2−222−2−22000000000000
χ282222-2-222-2-2-2-20000-2-222−2−222−2−2000022002−22−2−2−222−2−222-22-220000−222−2−222−2000000000000
χ292222-2-222-2-2-2-20000-2-2−2−222−2−22200002200−22−2222−2−222−2−22-22-20000−222−2−222−2000000000000
χ302222-2-222-2-2-2-20000-2-2−2−222−2−22200002200−22−2222−2−222−2−2-22-2200002−2−222−2−22000000000000
χ312222-2-2-2-2220022220022222222000000-2-2-2-2-2-2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ322222-2-2-2-2220022220022222222000000-2-2-2-2-2-2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ332222-2-2-2-22200222200-2-2-2-2-2-2-2-2000000-2-22222000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ342222-2-2-2-22200222200-2-2-2-2-2-2-2-2000000-2-22222000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ3522-2-22-2-222-22222-2-2-2-22222-2-2-2-2-2-222-22-2222-2-2-2-2-2-222220000000000000000000000000000
χ3622-2-22-2-222-22222-2-2-2-2-2-2-2-22222-2-222-22-22-2-2222222-2-2-2-20000000000000000000000000000
χ3722-2-22-2-222-222-2-222-2-20000000022-2-2-222-20000000000000000000022-2-2-2-222000000000000
χ3822-2-22-2-222-222-2-222-2-20000000022-2-2-222-200000000000000000000-2-22222-2-2000000000000
χ3922-2-22-2-222-2-2-2-2-2222200000000-2-2222-22-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4022-2-22-2-222-2-2-2-2-2222200000000-2-2222-22-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4122-2-2-222-22-20022-2-2002222-2-2-2-20000002-2-2-222000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ4222-2-2-222-22-20022-2-2002222-2-2-2-20000002-2-2-222000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ4322-2-2-222-22-20022-2-200-2-2-2-222220000002-222-2-2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ4422-2-2-222-22-20022-2-200-2-2-2-222220000002-222-2-2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ4522-2-2-22-22-22220000-2-222−2−2−2−22200002-2002−2−22−2−22222−2−22i−2i−2i2i0000i2−i2−i2i2−i2i2i2−i2000000000000
χ4622-2-2-22-22-22220000-2-222−2−2−2−22200002-2002−2−22−2−22222−2−2−2i2i2i−2i0000−i2i2i2−i2i2−i2−i2i2000000000000
χ4722-2-2-22-22-22220000-2-2−2−22222−2−200002-200−222−222−2−2−2−2222i−2i−2i2i0000−i2i2i2−i2i2−i2−i2i2000000000000
χ4822-2-2-22-22-22220000-2-2−2−22222−2−200002-200−222−222−2−2−2−222−2i2i2i−2i0000i2−i2−i2i2−i2i2i2−i2000000000000
χ4922-2-2-22-22-22-2-200002222−2−2−2−2220000-22002−2−2222−2−2−2−22200002-2-222−22−2−22−22000000000000
χ5022-2-2-22-22-22-2-200002222−2−2−2−2220000-22002−2−2222−2−2−2−2220000-222-2−22−222−22−2000000000000
χ5122-2-2-22-22-22-2-2000022−2−22222−2−20000-2200−222−2−2−22222−2−200002-2-22−22−222−22−2000000000000
χ5222-2-2-22-22-22-2-2000022−2−22222−2−20000-2200−222−2−2−22222−2−20000-222-22−22−2−22−22000000000000
χ53444444-4-4-4-4000000002222−22−222222−22−2200000000−2222−2222000000000000000000000000000000000000
χ54444444-4-4-4-400000000−22−222222−22−2222220000000022−2222−22000000000000000000000000000000000000
χ554444-4-4-4-44400-4-4-4-40000000000000000440000000000000000000000000000000000000000
χ5644-4-44-44-4-44000000002222−22−22−22−22222200000000−222222−22000000000000000000000000000000000000
χ5744-4-44-44-4-4400000000−22−2222222222−22−220000000022−22−2222000000000000000000000000000000000000
χ5844-4-4-444-44-400-4-4440000000000000000-440000000000000000000000000000000000000000
χ594-44-40000002i2−2i222−2222−222i2−2i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52i−2i2i−2i00000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ604-44-40000002i2−2i222−2222−222i2−2i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52i−2i2i−2i00000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ614-44-40000002i2−2i2−2222−22222i2−2i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2i2i−2i2i00000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000000000000000
χ624-44-40000002i2−2i2−2222−22222i2−2i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2i2i−2i2i00000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000000000000000
χ634-44-4000000−2i22i222−2222−22−2i22i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2i2i−2i2i00000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ644-44-4000000−2i22i222−2222−22−2i22i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2i2i−2i2i00000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ654-44-4000000−2i22i2−2222−2222−2i22i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72i−2i2i−2i00000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000000000000000
χ664-44-4000000−2i22i2−2222−2222−2i22i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72i−2i2i−2i00000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000000000000000
χ674-4-440000002i2−2i222−22−2222−2i22i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2i2i2i−2i00000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ684-4-440000002i2−2i222−22−2222−2i22i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2i2i2i−2i00000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ694-4-440000002i2−2i2−222222−22−2i22i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72i−2i−2i2i00000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000000000000000
χ704-4-440000002i2−2i2−222222−22−2i22i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72i−2i−2i2i00000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000000000000000
χ714-4-44000000−2i22i222−22−22222i2−2i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52i−2i−2i2i00000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ724-4-44000000−2i22i222−22−22222i2−2i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52i−2i−2i2i00000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ734-4-44000000−2i22i2−222222−222i2−2i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2i2i2i−2i00000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000000000000000
χ744-4-44000000−2i22i2−222222−222i2−2i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2i2i2i−2i00000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000000000000000

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