Finite Group Databasebeta

← Group #146270

Character table — Group #146270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444488884444888888888888881616161616161616161616161616161644448888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222222-2-2-2-222-2-2-2-2000000002222-2-2-2-20000000000000000
χ1022222222222222-2-2-2-222-2-2-2-200000000-2-2-2-222220000000000000000
χ112222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ122222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ132222222222-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-200000000
χ142222222222-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2222200000000
χ15222222-2-2-2-200002-22-200000000002i2i−2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ16222222-2-2-2-200002-22-200000000002i2i−2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ17222222-2-2-2-200002-22-20000000000−2i−2i2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ18222222-2-2-2-200002-22-20000000000−2i−2i2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ19222222-2-2-2-20000-22-220000002i2i−2i−2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000
χ20222222-2-2-2-20000-22-220000002i2i−2i−2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000
χ21222222-2-2-2-20000-22-22000000−2i−2i2i2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000
χ22222222-2-2-2-20000-22-22000000−2i−2i2i2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000
χ232222-2-222-2-2222222-2-2-2-2-2-22200000000000000000000000000002i−2i00
χ242222-2-222-2-2222222-2-2-2-2-2-2220000000000000000000000000000−2i2i00
χ252222-2-222-2-22222-2-222-2-222-2-20000000000000000000000000000002i−2i
χ262222-2-222-2-22222-2-222-2-222-2-2000000000000000000000000000000−2i2i
χ272222-2-222-2-2-2-2-2-222-2-22222-2-20000000000000000000000002-2000000
χ282222-2-222-2-2-2-2-2-222-2-22222-2-2000000000000000000000000-22000000
χ292222-2-222-2-2-2-2-2-2-2-22222-2-222000000000000000000000000002i−2i0000
χ302222-2-222-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000−2i2i0000
χ3122-2-2-222-22-200000000002-22-22−22−22−22−2i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i00000000
χ3222-2-2-222-22-200000000002-22-22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i00000000
χ3322-2-2-222-22-200000000002-22-2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i00000000
χ3422-2-2-222-22-200000000002-22-2−22−22−22−22−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i00000000
χ3522-2-2-222-22-20000000000-22-222−22−2−22−22i2−i2i2−i2−i2i2−i2i22i−2i2i−2i000000000000
χ3622-2-2-222-22-20000000000-22-222−22−2−22−22−i2i2−i2i2i2−i2i2−i2−2i2i−2i2i000000000000
χ3722-2-2-222-22-20000000000-22-22−22−222−22−2i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i000000000000
χ3822-2-2-222-22-20000000000-22-22−22−222−22−2−i2i2−i2i2i2−i2i2−i22i−2i2i−2i000000000000
χ3922-2-2-22-22-2222-2-200002-20000i2−i2−i2i2i2−i2−i2i200002i−2i−2i2i−222−2−222−200000000
χ4022-2-2-22-22-2222-2-200002-20000i2−i2−i2i2i2−i2−i2i20000−2i2i2i−2i2−2−222−2−2200000000
χ4122-2-2-22-22-2222-2-200002-20000−i2i2i2−i2−i2i2i2−i200002i−2i−2i2i2−2−222−2−2200000000
χ4222-2-2-22-22-2222-2-200002-20000−i2i2i2−i2−i2i2i2−i20000−2i2i2i−2i−222−2−222−200000000
χ4322-2-2-22-22-22-2-2220000-220000i2−i2−i2i2−i2i2i2−i22i−2i−2i2i0000−222−22−2−2200000000
χ4422-2-2-22-22-22-2-2220000-220000i2−i2−i2i2−i2i2i2−i2−2i2i2i−2i00002−2−22−222−200000000
χ4522-2-2-22-22-22-2-2220000-220000−i2i2i2−i2i2−i2−i2i22i−2i−2i2i00002−2−22−222−200000000
χ4622-2-2-22-22-22-2-2220000-220000−i2i2i2−i2i2−i2−i2i2−2i2i2i−2i0000−222−22−2−2200000000
χ474444-4-4-4-44400004-4-4400000000000000000000000000000000000000
χ484444-4-4-4-4440000-444-400000000000000000000000000000000000000
χ4944-4-44-44-4-4400000000004-4-4400000000000000000000000000000000
χ5044-4-44-44-4-440000000000-444-400000000000000000000000000000000
χ5144-4-44-4-444-444-4-40000-44000000000000000000000000000000000000
χ5244-4-44-4-444-4-4-44400004-4000000000000000000000000000000000000
χ538-88-800000042−4242−42000000000000000000000000000000000000000000
χ548-88-8000000−4242−4242000000000000000000000000000000000000000000
χ558-8-8800000042−42−4242000000000000000000000000000000000000000000
χ568-8-88000000−424242−42000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).