Finite Group Databasebeta

← Group #145913

Character table — Group #145913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888448888888888888888888816161616161616161616161616161616444488884444
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
χ112222222222-2-222-2-222222222-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ122222222222-2-222-2-222222222-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ132222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i2i−2i−2i0000
χ142222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i−2i2i2i0000
χ1522222222-2-222-2-22200000000-2-200002222-2-2-2-2000000002222−2−2−2−22222−2−2−2−2000000000000
χ1622222222-2-222-2-22200000000-2-200002222-2-2-2-200000000−2−2−2−22222−2−2−2−22222000000000000
χ1722222222-2-222-2-22200000000-2-20000-2-2-2-22222000000002222−2−2−2−2−2−2−2−22222000000000000
χ1822222222-2-222-2-22200000000-2-20000-2-2-2-2222200000000−2−2−2−222222222−2−2−2−2000000000000
χ19222-2-2-22-2002-200-2222−2−222−2−20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000
χ20222-2-2-22-2002-200-2222−2−222−2−20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000
χ21222-2-2-22-2002-200-2222−2−222−2−20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000
χ22222-2-2-22-2002-200-2222−2−222−2−20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000
χ23222-2-2-22-2002-200-22−2−222−2−22200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000
χ24222-2-2-22-2002-200-22−2−222−2−22200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000
χ25222-2-2-22-2002-200-22−2−222−2−22200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000
χ26222-2-2-22-2002-200-22−2−222−2−22200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000
χ272-222-2-2-2222-2-2-2-222000000002-20000000000002i2i−2i−2i2i2i−2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ282-222-2-2-2222-2-2-2-222000000002-20000000000002i2i−2i−2i2i2i−2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ292-222-2-2-2222-2-2-2-222000000002-2000000000000−2i−2i2i2i−2i−2i2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ302-222-2-2-2222-2-2-2-222000000002-2000000000000−2i−2i2i2i−2i−2i2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ312-222-2-2-22-2-22222-2-22222-2-2-2-22-22-22-20000000000000000000000000000000000000000002-2
χ322-222-2-2-22-2-22222-2-22222-2-2-2-22-22-22-2000000000000000000000000000000000000000000-22
χ332-222-2-2-22-2-22222-2-2-2-2-2-222222-2-22-2200000000000000000000000000000000000000002i−2i00
χ342-222-2-2-22-2-22222-2-2-2-2-2-222222-2-22-220000000000000000000000000000000000000000−2i2i00
χ352-222-2-2-22-2-2-2-222222222-2-2-2-2-22-22-220000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ362-222-2-2-22-2-2-2-222222222-2-2-2-2-22-22-22000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ372-222-2-2-22-2-2-2-22222-2-2-2-22222-222-22-200000000000000002-22-2-22-2200000000000000000000
χ382-222-2-2-22-2-2-2-22222-2-2-2-22222-222-22-20000000000000000-22-222-22-200000000000000000000
χ392-22-222-2-200-2200-2222−2−2−2−22200−222−2000022-2-222−2−2−2−222ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ402-22-222-2-200-2200-2222−2−2−2−22200−222−2000022-2-222−2−2−2−222−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ412-22-222-2-200-2200-2222−2−2−2−22200−222−20000-2-222−2−22222−2−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ422-22-222-2-200-2200-2222−2−2−2−22200−222−20000-2-222−2−22222−2−2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ432-22-222-2-200-2200-22−2−22222−2−2002−2−22000022-2-2−2−22222−2−2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7000000000000
χ442-22-222-2-200-2200-22−2−22222−2−2002−2−22000022-2-2−2−22222−2−2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7000000000000
χ452-22-222-2-200-2200-22−2−22222−2−2002−2−220000-2-22222−2−2−2−222ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7000000000000
χ462-22-222-2-200-2200-22−2−22222−2−2002−2−220000-2-22222−2−2−2−222−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7000000000000
χ472-2-222-22-22-2002-2002-22-22-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000002-2i2−i2i2−i20000
χ482-2-222-22-22-2002-2002-22-22-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000-22−i2i2−i2i20000
χ492-2-222-22-22-2002-2002-22-22-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000002-2−i2i2−i2i20000
χ502-2-222-22-22-2002-2002-22-22-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000-22i2−i2i2−i20000
χ512-2-222-22-22-2002-200-22-22-22-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000002i−2i002−2−220000
χ522-2-222-22-22-2002-200-22-22-22-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000−2i2i00−222−20000
χ532-2-222-22-22-2002-200-22-22-22-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000002i−2i00−222−20000
χ542-2-222-22-22-2002-200-22-22-22-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000−2i2i002−2−220000
χ5544444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ56444-4-4-44-400-44004-42222−22−222222−22−2200−22−22222200000000000000000000000000000000000000000000
χ57444-4-4-44-400-44004-4−22−222222−22−222222002222−22−2200000000000000000000000000000000000000000000
χ5844-44-44-4-44-400-4400000000000000000000000022−22−222222−22−22220000000000000000000000000000
χ5944-44-44-4-44-400-44000000000000000000000000−222222−22−222222−220000000000000000000000000000
χ6044-44-44-4-4-44004-4004-44-4-44-4400000000000000000000000000000000000000000000000000
χ6144-44-44-4-4-44004-400-44-444-44-400000000000000000000000000000000000000000000000000
χ6244-4-44-4-440000000022−22−2222−222222−2200000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ6344-4-44-4-440000000022−22−2222−222222−220000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ6444-4-44-4-4400000000−222222−2222−22−222200000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ6544-4-44-4-4400000000−222222−2222−22−22220000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ664-444-4-4-444444-4-4-4-400000000-44000000000000000000000000000000000000000000000000
χ674-44-444-4-4004-4004-42222−22−22−22−2222220022−22−222200000000000000000000000000000000000000000000
χ684-44-444-4-4004-4004-4−22−2222222222−22−2200−222222−2200000000000000000000000000000000000000000000
χ694-4-444-44-4-4400-4400000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ704-4-444-44-4-4400-440000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ714-4-4-4-44440000000022−22−222222−22−222200000022−22−222200002-22-2-22-220000000000000000000000000000
χ724-4-4-4-44440000000022−22−222222−22−2222000000−222222−220000-22-222-22-20000000000000000000000000000
χ734-4-4-4-444400000000−222222−22−222222−2200000022−22−22220000-22-222-22-20000000000000000000000000000
χ744-4-4-4-444400000000−222222−22−222222−22000000−222222−2200002-22-2-22-220000000000000000000000000000

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