Finite Group Databasebeta

← Group #146231

Character table — Group #146231

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444444444488888888888888881616161616161616161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
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
χ92222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ102222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ11222222222-2-2-2-22-2-222-2-222-2-200000000000000002222-2-2-2-200000000
χ12222222222-2-2-2-22-2-222-2-222-2-20000000000000000-2-2-2-2222200000000
χ13222222222-2-2-2-22-2-2-2-222-2-222000000002222-2-2-2-20000000000000000
χ14222222222-2-2-2-22-2-2-2-222-2-22200000000-2-2-2-222220000000000000000
χ15222222-2-2-222-2-2-22-200000000000022-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ16222222-2-2-222-2-2-22-200000000000022-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ17222222-2-2-222-2-2-22-2000000000000-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ18222222-2-2-222-2-2-22-2000000000000-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ19222222-2-2-2-2-222-2-220000000022-2-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ20222222-2-2-2-2-222-2-220000000022-2-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ21222222-2-2-2-2-222-2-2200000000-2-2220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ22222222-2-2-2-2-222-2-2200000000-2-2220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ232222-2-2-2222222-2-2-222-2-2-2-2220000000000000000000000000000002i−2i
χ242222-2-2-2222222-2-2-222-2-2-2-222000000000000000000000000000000−2i2i
χ252222-2-2-2222222-2-2-2-2-22222-2-200000000000000000000000000002i−2i00
χ262222-2-2-2222222-2-2-2-2-22222-2-20000000000000000000000000000−2i2i00
χ272222-2-2-222-2-2-2-2-2222222-2-2-2-20000000000000000000000002-2000000
χ282222-2-2-222-2-2-2-2-2222222-2-2-2-2000000000000000000000000-22000000
χ292222-2-2-222-2-2-2-2-222-2-2-2-22222000000000000000000000000002i−2i0000
χ302222-2-2-222-2-2-2-2-222-2-2-2-2222200000000000000000000000000−2i2i0000
χ3122-2-2-2222-20000-200002-2002-22−22−22−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000
χ3222-2-2-2222-20000-200002-2002-22−22−22−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000
χ3322-2-2-2222-20000-200002-2002-2−22−22−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000
χ3422-2-2-2222-20000-200002-2002-2−22−22−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000
χ3522-2-2-2222-20000-20000-2200-222−22−2−22−222i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i200000000
χ3622-2-2-2222-20000-20000-2200-222−22−2−22−22−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i200000000
χ3722-2-2-2222-20000-20000-2200-22−22−222−22−22i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i200000000
χ3822-2-2-2222-20000-20000-2200-22−22−222−22−2−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i200000000
χ3922-2-2-22-2-2200002002-2002-2002−2−222−2−222−2−222−2−2200002-2-2200000000
χ4022-2-2-22-2-2200002002-2002-2002−2−222−2−22−222−2−222−20000-222-200000000
χ4122-2-2-22-2-2200002002-2002-200−222−2−222−22−2−222−2−220000-222-200000000
χ4222-2-2-22-2-2200002002-2002-200−222−2−222−2−222−2−222−200002-2-2200000000
χ4322-2-2-22-2-220000200-2200-22002−2−22−222−22−2−22−222−22-2-22000000000000
χ4422-2-2-22-2-220000200-2200-22002−2−22−222−2−222−22−2−22-222-2000000000000
χ4522-2-2-22-2-220000200-2200-2200−222−22−2−222−2−22−222−2-222-2000000000000
χ4622-2-2-22-2-220000200-2200-2200−222−22−2−22−222−22−2−222-2-22000000000000
χ474444-4-44-4-444-4-44-440000000000000000000000000000000000000000
χ484444-4-44-4-4-4-44444-40000000000000000000000000000000000000000
χ4944-4-44-44-440000-4004-400-440000000000000000000000000000000000
χ5044-4-44-44-440000-400-44004-40000000000000000000000000000000000
χ5144-4-44-4-44-40000400004-400-4400000000000000000000000000000000
χ5244-4-44-4-44-4000040000-44004-400000000000000000000000000000000
χ538-88-800000008-80000000000000000000000000000000000000000000
χ548-88-80000000-880000000000000000000000000000000000000000000
χ558-8-88000008-8000000000000000000000000000000000000000000000
χ568-8-8800000-88000000000000000000000000000000000000000000000

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