Finite Group Databasebeta

← Group #506382

Character table — Group #506382

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order122222444488888888161616161616161644448888161616161616161616161616224488881616161616161616224488884444
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ9111111111111-1-1-1-11111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ10111111111111-1-1-1-11111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ11111111111111-1-1-1-11111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111111111-1-1-1-1-11-11
χ12111111111111-1-1-1-11111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111-1-1-1-111111-11-1
χ13111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111111-11-111-1-1-1-1-1-111111-11-1-1-1111-1-11
χ14111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111111-11-111-1-1-1-1-1-11111-11-1111-1-1-111-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-11-11-1-1111111-1-1-1-11-11-1-1-111-111-1
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-11-11-1-1111111-1-1-1-1-11-1111-1-11-1-11
χ172222222222-2-22222-2-200000000-2-2-2-2-222-20000000000002222-2-2-2-200000000000000000000
χ182222222222-2-22222-2-200000000-2-2-2-2-222-2000000000000-2-2-2-2222200000000000000000000
χ192222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000002-22-2-2-22200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000-22-2222-2-200000000000000000000
χ212222-2-22-22-222000022222222220000-200-2-2-2-2-200000000000000000000000022-2-200000000
χ222222-2-22-22-222000022222222220000-200-2-2-2-2-2000000000000000000000000-2-22200000000
χ232222-2-22-22-222000022-2-2-2-2-2-2-2-20000-200-222220000000000000000000000002-2-2200000000
χ242222-2-22-22-222000022-2-2-2-2-2-2-2-20000-200-22222000000000000000000000000-222-200000000
χ252222-2-2-22-22002222002222−2−2−2−200000-2-2022−2−22222−2−2−2−22-2-22000022−2−222−2−2000000000000
χ262222-2-2-22-22002222002222−2−2−2−200000-2-2022−2−22222−2−2−2−2-222-20000−2−222−2−222000000000000
χ272222-2-2-22-2200222200−2−2−2−2222200000-2-20−2−222−2−2−2−222222-2-220000−2−222−2−222000000000000
χ282222-2-2-22-2200222200−2−2−2−2222200000-2-20−2−222−2−2−2−22222-222-2000022−2−222−2−2000000000000
χ292222-2-2-22-2200-2-2-2-2002222−2−2−2−20000022022−2−2−2−2−2−2222222-2-2000022−2−2−2−222000000000000
χ302222-2-2-22-2200-2-2-2-2002222−2−2−2−20000022022−2−2−2−2−2−22222-2-2220000−2−22222−2−2000000000000
χ312222-2-2-22-2200-2-2-2-200−2−2−2−2222200000220−2−2222222−2−2−2−222-2-20000−2−22222−2−2000000000000
χ322222-2-2-22-2200-2-2-2-200−2−2−2−2222200000220−2−2222222−2−2−2−2-2-222000022−2−2−2−222000000000000
χ3322-2-22-22-2-220022-2-20022−2−222−2−2000002-202−22−222−2−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ3422-2-22-22-2-220022-2-20022−2−222−2−2000002-202−22−222−2−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ3522-2-22-22-2-220022-2-200−2−222−2−222000002-20−22−22−2−222−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ3622-2-22-22-2-220022-2-200−2−222−2−222000002-20−22−22−2−222−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ3722-2-22-22-2-2200-2-2220022−2−222−2−200000-2202−22−2−2−222−2−22200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2000000000000
χ3822-2-22-22-2-2200-2-2220022−2−222−2−200000-2202−22−2−2−222−2−2220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2000000000000
χ3922-2-22-22-2-2200-2-22200−2−222−2−22200000-220−22−2222−2−222−2−200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2000000000000
χ4022-2-22-22-2-2200-2-22200−2−222−2−22200000-220−22−2222−2−222−2−20000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2000000000000
χ4122-2-22-2-222-2-2-200002222-2-2-2-2220000200-2-222-200000000000000000000000000002i−2i2i−2i0000
χ4222-2-22-2-222-2-2-200002222-2-2-2-2220000200-2-222-20000000000000000000000000000−2i2i−2i2i0000
χ4322-2-22-2-222-2-2-2000022-2-22222-2-20000200-22-2-2200000000000000000000000000002i−2i−2i2i0000
χ4422-2-22-2-222-2-2-2000022-2-22222-2-20000200-22-2-220000000000000000000000000000−2i2i2i−2i0000
χ4522-2-2-22-2-2222222-2-2-2-20000000022-2-22-22-2000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ4622-2-2-22-2-2222222-2-2-2-20000000022-2-22-22-200000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ4722-2-2-22-2-22222-2-222-2-200000000-2-22222-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ4822-2-2-22-2-22222-2-222-2-200000000-2-22222-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ4922-2-2-22-2-222-2-222-2-22222-2-2-2-222-2-222-2-2222-2-2222-2-2-2-2220000000000000000000000000000
χ5022-2-2-22-2-222-2-222-2-222-2-22222-2-2-2-222-2-222-222-2-2-22222-2-20000000000000000000000000000
χ5122-2-2-22-2-222-2-2-2-2222222-2-2-2-22222-2-2-22-222-2-22-2-22222-2-20000000000000000000000000000
χ5222-2-2-22-2-222-2-2-2-22222-2-22222-2-222-2-2-22-22-222-222-2-2-2-2220000000000000000000000000000
χ53444444-4-4-4-40000000022222222−22−22−22−2200000000−22−222222000000000000000000000000000000000000
χ54444444-4-4-4-400000000−22−22−22−2222222222000000002222−22−22000000000000000000000000000000000000
χ554444-4-44-44-4-4-40000-4-400000000000040040000000000000000000000000000000000000000
χ5644-4-44-4-444-4440000-4-4000000000000-40040000000000000000000000000000000000000000
χ5744-4-4-4444-4-4000000002222−22−222222−22−2200000000−2222−2222000000000000000000000000000000000000
χ5844-4-4-4444-4-400000000−22−222222−22−2222220000000022−2222−22000000000000000000000000000000000000
χ594-44-400000022−222i2−2i22i2−2i222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+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
χ604-44-400000022−222i2−2i22i2−2i222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+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
χ614-44-400000022−22−2i22i2−2i22i222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+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
χ624-44-400000022−22−2i22i2−2i22i222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+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
χ634-44-4000000−22222i2−2i22i2−2i2−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2i2i−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
χ644-44-4000000−22222i2−2i22i2−2i2−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7−2i2i−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
χ654-44-4000000−2222−2i22i2−2i22i2−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ72i−2i2i−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
χ664-44-4000000−2222−2i22i2−2i22i2−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72i−2i2i−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
χ674-4-4400000022−222i2−2i2−2i22i2−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72i−2i−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
χ684-4-4400000022−222i2−2i2−2i22i2−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72i−2i−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
χ694-4-4400000022−22−2i22i22i2−2i2−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2i2i2i−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
χ704-4-4400000022−22−2i22i22i2−2i2−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2i2i2i−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
χ714-4-44000000−22222i2−2i2−2i22i222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2i2i2i−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
χ724-4-44000000−22222i2−2i2−2i22i222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2i2i2i−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
χ734-4-44000000−2222−2i22i22i2−2i222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52i−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
χ744-4-44000000−2222−2i22i22i2−2i222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52i−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

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