Finite Group Databasebeta

← Group #145367

Character table — Group #145367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888448888888888888888888816161616161616161616161616161616224488882244
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ92222222222222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ112222222222-222-2-2-222222222-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ122222222222-222-2-2-222222222-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ132222222222-222-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i2i−2i−2i0000
χ142222222222-222-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i−2i2i2i0000
χ1522222222-2-22-2-222200000000-2-200002222-2-2-2-2000000002222−2−2−2−22222−2−2−2−2000000000000
χ1622222222-2-22-2-222200000000-2-200002222-2-2-2-200000000−2−2−2−22222−2−2−2−22222000000000000
χ1722222222-2-22-2-222200000000-2-20000-2-2-2-22222000000002222−2−2−2−2−2−2−2−22222000000000000
χ1822222222-2-22-2-222200000000-2-20000-2-2-2-2222200000000−2−2−2−222222222−2−2−2−2000000000000
χ19222-2-2-22-2002002-2-2222−2−2−22−20022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000000000
χ20222-2-2-22-2002002-2-2222−2−2−22−20022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000000000
χ21222-2-2-22-2002002-2-2222−2−2−22−20022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000000000
χ22222-2-2-22-2002002-2-2222−2−2−22−20022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000000000
χ23222-2-2-22-2002002-2-2−2−2−2222−2200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000000000
χ24222-2-2-22-2002002-2-2−2−2−2222−2200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000000000
χ25222-2-2-22-2002002-2-2−2−2−2222−2200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000000000
χ26222-2-2-22-2002002-2-2−2−2−2222−2200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000000000
χ2722-2-22-2-222-202-200022-222-2-2-200000022−2−22−22−222−2−222−2−20000000000000000002i−2ii2−i2i2−i20000
χ2822-2-22-2-222-202-200022-222-2-2-200000022−2−22−22−222−2−222−2−2000000000000000000−2i2i−i2i2−i2i20000
χ2922-2-22-2-222-202-200022-222-2-2-2000000−2−222−22−22−2−222−2−2220000000000000000002i−2i−i2i2−i2i20000
χ3022-2-22-2-222-202-200022-222-2-2-2000000−2−222−22−22−2−222−2−222000000000000000000−2i2ii2−i2i2−i20000
χ3122-2-22-2-222-202-2000-2-22-2-222200000022−2−22−22−2−2−222−2−22200000000000000002-2002−2−220000
χ3222-2-22-2-222-202-2000-2-22-2-222200000022−2−22−22−2−2−222−2−2220000000000000000-2200−222−20000
χ3322-2-22-2-222-202-2000-2-22-2-2222000000−2−222−22−2222−2−222−2−200000000000000002-200−222−20000
χ3422-2-22-2-222-202-2000-2-22-2-2222000000−2−222−22−2222−2−222−2−20000000000000000-22002−2−220000
χ352-2-22-2-22200-2002-222−222−2−2−22002−22−22-22-200002−22−22−22−2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000000000000
χ362-2-22-2-22200-2002-222−222−2−2−22002−22−22-22-200002−22−22−22−2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000000000000
χ372-2-22-2-22200-2002-222−222−2−2−22002−22−2-22-220000−22−22−22−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000000000000
χ382-2-22-2-22200-2002-222−222−2−2−22002−22−2-22-220000−22−22−22−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000000000000
χ392-2-22-2-22200-2002-22−22−2−2222−200−22−222-22-20000−22−22−22−22ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000000000000
χ402-2-22-2-22200-2002-22−22−2−2222−200−22−222-22-20000−22−22−22−22−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000000000000
χ412-2-22-2-22200-2002-22−22−2−2222−200−22−22-22-2200002−22−22−22−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000000000000
χ422-2-22-2-22200-2002-22−22−2−2222−200−22−22-22-2200002−22−22−22−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000000000000
χ432-2-2-2222-222-2-2-222-2000000002-20000000000002i−2i2i−2i−2i2i−2i2i2−2−222−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ442-2-2-2222-222-2-2-222-2000000002-20000000000002i−2i2i−2i−2i2i−2i2i−222−2−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ452-2-2-2222-222-2-2-222-2000000002-2000000000000−2i2i−2i2i2i−2i2i−2i2−2−222−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ462-2-2-2222-222-2-2-222-2000000002-2000000000000−2i2i−2i2i2i−2i2i−2i−222−2−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-2-2222-2-2-2222-2-222-22-222-2-22-2-222-20000000000000000000000000000000000000000002i−2i
χ482-2-2-2222-2-2-2222-2-222-22-222-2-22-2-222-2000000000000000000000000000000000000000000−2i2i
χ492-2-2-2222-2-2-2222-2-22-22-22-2-2222-22-2-2200000000000000000000000000000000000000002-200
χ502-2-2-2222-2-2-2222-2-22-22-22-2-2222-22-2-220000000000000000000000000000000000000000-2200
χ512-2-2-2222-2-2-2-22222-22-22-222-2-2-222-2-220000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ522-2-2-2222-2-2-2-22222-22-22-222-2-2-222-2-22000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ532-2-2-2222-2-2-2-22222-2-22-22-2-222-22-222-200000000000000002-2-22-222-200000000000000000000
χ542-2-2-2222-2-2-2-22222-2-22-22-2-222-22-222-20000000000000000-222-22-2-2200000000000000000000
χ5544444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ56444-4-4-44-400-400-444222222−22−22−2222−2200−22−22222200000000000000000000000000000000000000000000
χ57444-4-4-44-400-400-444−22−22−22222222−2222002222−22−2200000000000000000000000000000000000000000000
χ5844-44-44-4-4000000002222−22−22−2222−222200000000002i2−2i2−2i22i22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ5944-44-44-4-4000000002222−22−22−2222−22220000000000−2i22i22i2−2i2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6044-44-44-4-400000000−22−22222222−2222−2200000000002i2−2i2−2i22i2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6144-44-44-4-400000000−22−22222222−2222−220000000000−2i22i22i2−2i22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ6244-4-44-4-44-440-44000000000000000002222−22−22−2222−2222000000000000000000000000000000000000
χ6344-4-44-4-44-440-4400000000000000000−22−22222222−2222−22000000000000000000000000000000000000
χ644-4444-4-4-44-40-4400000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ654-4444-4-4-44-40-440000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ664-4444-4-4-4-4404-40004-4-4-44-44400000000000000000000000000000000000000000000000000
χ674-4444-4-4-4-4404-4000-4444-44-4-400000000000000000000000000000000000000000000000000
χ684-44-4-44-440000000022−22−2222−222222−2200000022−22−222200002-2-222-2-220000000000000000000000000000
χ694-44-4-44-440000000022−22−2222−222222−22000000−222222−220000-222-2-222-20000000000000000000000000000
χ704-44-4-44-4400000000−222222−2222−22−222200000022−22−22220000-222-2-222-20000000000000000000000000000
χ714-44-4-44-4400000000−222222−2222−22−2222000000−222222−2200002-2-222-2-220000000000000000000000000000
χ724-4-44-4-44400400-44-422−222222−22−22−222200−2222−222200000000000000000000000000000000000000000000
χ734-4-44-4-44400400-44-4−2222−22−22222222−220022−2222−2200000000000000000000000000000000000000000000
χ744-4-4-4444-4444-4-4-4-4400000000-44000000000000000000000000000000000000000000000000

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