Finite Group Databasebeta

← Group #145266

Character table — Group #145266

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12222244444444888888884488881616161616161616161616161616161622448888161616161616161644888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000
χ112222222-2-2-2-222200000000-2-2000022222222−2−2−2−2−2−2−2−222-2-200002222−2−2−2−200000000
χ122222222-2-2-2-222200000000-2-2000022222222−2−2−2−2−2−2−2−2-2-2220000−2−2−2−2222200000000
χ132222222-2-2-2-222200000000-2-20000−2−2−2−2−2−2−2−22222222222-2-20000−2−2−2−2222200000000
χ142222222-2-2-2-222200000000-2-20000−2−2−2−2−2−2−2−222222222-2-22200002222−2−2−2−200000000
χ15222222-22222-2-2-222222222-2-2-2-2-2-200000000000000000000000000000000002i−2i0000
χ16222222-22222-2-2-222222222-2-2-2-2-2-20000000000000000000000000000000000−2i2i0000
χ17222222-22222-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000002i−2i
χ18222222-22222-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000−2i2i
χ192222-2-2222-2-22-2-2000000002-200002222−2−2−2−22222−2−2−2−200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i200000000
χ202222-2-2222-2-22-2-2000000002-200002222−2−2−2−22222−2−2−2−20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i200000000
χ212222-2-2222-2-22-2-2000000002-20000−2−2−2−22222−2−2−2−2222200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i200000000
χ222222-2-2222-2-22-2-2000000002-20000−2−2−2−22222−2−2−2−222220000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i200000000
χ232222-2-22-2-2222-2-22222-2-2-2-2-2222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ242222-2-22-2-2222-2-22222-2-2-2-2-2222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ252222-2-22-2-2222-2-2-2-2-2-22222-22-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ262222-2-22-2-2222-2-2-2-2-2-22222-22-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ272222-2-2-2-2-222-2222222-2-2-2-22-2-2-2220000000000000000000000000000000000002-200
χ282222-2-2-2-2-222-2222222-2-2-2-22-2-2-222000000000000000000000000000000000000-2200
χ292222-2-2-2-2-222-222-2-2-2-222222-222-2-2000000000000000000000000000000002-2000000
χ302222-2-2-2-2-222-222-2-2-2-222222-222-2-200000000000000000000000000000000-22000000
χ3122-2-22-2-2000022-222−2−22−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5002i−2ii2−i2i2−i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ3222-2-22-2-2000022-222−2−22−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500−2i2i−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ3322-2-22-2-2000022-222−2−22−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5002i−2ii2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ3422-2-22-2-2000022-222−2−22−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500−2i2i−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ3522-2-22-2-2000022-2−2−222−22−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7002i−2i−i2i2−i2i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ3622-2-22-2-2000022-2−2−222−22−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700−2i2ii2−i2i2−i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ3722-2-22-2-2000022-2−2−222−22−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7002i−2i−i2i2−i2i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ3822-2-22-2-2000022-2−2−222−22−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700−2i2ii2−i2i2−i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ3922-2-2-22-200002-2222−2−2−22−22002−2−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ72-2002−2−22−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ4022-2-2-22-200002-2222−2−2−22−22002−2−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7-2200−222−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ4122-2-2-22-200002-2222−2−2−22−22002−2−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ72-2002−2−22ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ4222-2-2-22-200002-2222−2−2−22−22002−2−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7-2200−222−2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ4322-2-2-22-200002-22−2−2222−22−200−222−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ52-200−222−2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ4422-2-2-22-200002-22−2−2222−22−200−222−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5-22002−2−22ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ4522-2-2-22-200002-22−2−2222−22−200−222−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ52-200−222−2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ4622-2-2-22-200002-22−2−2222−22−200−222−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5-22002−2−22−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ47444444-4-4-4-4-4-4-4-4000000004400000000000000000000000000000000000000000000
χ484444-4-4-444-4-4-44400000000-4400000000000000000000000000000000000000000000
χ4944-4-44-440000-4-442222−22−2222−2222−2200−2222−22220000000000000000000000000000000000000000
χ5044-4-44-440000-4-44−22−222222−2222−22220022−2222−220000000000000000000000000000000000000000
χ5144-4-4-4440000-44-42222−22−22−2222−222200−222222−220000000000000000000000000000000000000000
χ5244-4-4-4440000-44-4−22−22222222−2222−220022−22−22220000000000000000000000000000000000000000
χ534-44-40004i−4i000002i2−2i22i2−2i222−22−2222000000ζ+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+ζ7ζ+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−ζ7000000000000000000000000
χ544-44-40004i−4i000002i2−2i22i2−2i222−22−2222000000−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−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−ζ7ζ−ζ3−ζ5+ζ7000000000000000000000000
χ554-44-40004i−4i00000−2i22i2−2i22i2−222222−22000000ζ−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+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−ζ7ζ+ζ3+ζ5+ζ7000000000000000000000000
χ564-44-40004i−4i00000−2i22i2−2i22i2−222222−22000000−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−ζ7ζ−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−ζ7000000000000000000000000
χ574-44-4000−4i4i000002i2−2i22i2−2i2−222222−22000000ζ−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−ζ7ζ−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+ζ7000000000000000000000000
χ584-44-4000−4i4i000002i2−2i22i2−2i2−222222−22000000−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+ζ7−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−ζ7000000000000000000000000
χ594-44-4000−4i4i00000−2i22i2−2i22i222−22−2222000000ζ+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−ζ7−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−ζ7000000000000000000000000
χ604-44-4000−4i4i00000−2i22i2−2i22i222−22−2222000000−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+ζ7ζ+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+ζ7000000000000000000000000
χ614-4-44000004-40004i−4i−4i4i00000000002-2-222i−2i−2i2i−2i2i2i−2i-222-2000000000000000000000000
χ624-4-44000004-40004i−4i−4i4i0000000000-222-2−2i2i2i−2i2i−2i−2i2i2-2-22000000000000000000000000
χ634-4-44000004-4000−4i4i4i−4i00000000002-2-22−2i2i2i−2i2i−2i−2i2i-222-2000000000000000000000000
χ644-4-44000004-4000−4i4i4i−4i0000000000-222-22i−2i−2i2i−2i2i2i−2i2-2-22000000000000000000000000
χ654-4-4400000-44000000044-4-400000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ664-4-4400000-44000000044-4-40000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ674-4-4400000-440000000-4-44400000022−22−22220000000022−22−2222000000000000000000000000
χ684-4-4400000-440000000-4-444000000−222222−2200000000−222222−22000000000000000000000000

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