Finite Group Databasebeta

← Group #499024

Character table — Group #499024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222222224448888888888881616161616161616112222222224448888888888881616161616161616
order122224444888882488161616161616161644888888222224444888882488161616161616161644888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ9222222222-2-2-2-2-222-2-20000000000000000222222222-2-2-2-2-222-2-20000000000000000
χ10222222222-2-2-2-2-2-2-2220000000000000000222222222-2-2-2-2-2-2-2220000000000000000
χ11222-2-222-2-200000002i−2i22−2−2i2i2−i2−i200000000222-2-222-2-200000002i−2i22−2−2i2i2−i2−i200000000
χ12222-2-222-2-200000002i−2i−2−222−i2−i2i2i200000000222-2-222-2-200000002i−2i−2−222−i2−i2i2i200000000
χ13222-2-222-2-20000000−2i2i22−2−2−i2−i2i2i200000000222-2-222-2-20000000−2i2i22−2−2−i2−i2i2i200000000
χ14222-2-222-2-20000000−2i2i−2−222i2i2−i2−i200000000222-2-222-2-20000000−2i2i−2−222i2i2−i2−i200000000
χ15222-2-2-2-222222-2-200000000000000002-200222-2-2-2-222222-2-200000000000000002-200
χ16222-2-2-2-222222-2-20000000000000000-2200222-2-2-2-222222-2-20000000000000000-2200
χ17222-2-2-2-222-2-2-2220000000000002-2000000222-2-2-2-222-2-2-2220000000000002-2000000
χ18222-2-2-2-222-2-2-222000000000000-22000000222-2-2-2-222-2-2-222000000000000-22000000
χ1922-22-22-22-222-22-20000000000000000002i−2i22-22-22-22-222-22-20000000000000000002i−2i
χ2022-22-22-22-222-22-2000000000000000000−2i2i22-22-22-22-222-22-2000000000000000000−2i2i
χ2122-22-22-22-2-2-22-22000000000000002i−2i000022-22-22-22-2-2-22-22000000000000002i−2i0000
χ2222-22-22-22-2-2-22-2200000000000000−2i2i000022-22-22-22-2-2-22-2200000000000000−2i2i0000
χ2322-22-2-22-22000002-2002−22−22−22−20000000022-22-2-22-22000002-2002−22−22−22−200000000
χ2422-22-2-22-22000002-200−22−22−22−220000000022-22-2-22-22000002-200−22−22−22−2200000000
χ2522-22-2-22-2200000-22002−22−2−22−220000000022-22-2-22-2200000-22002−22−2−22−2200000000
χ2622-22-2-22-2200000-2200−22−222−22−20000000022-22-2-22-2200000-2200−22−222−22−200000000
χ2722-2-22-222-222-2-2200002-2-2200000000000022-2-22-222-222-2-2200002-2-22000000000000
χ2822-2-22-222-222-2-220000-222-200000000000022-2-22-222-222-2-220000-222-2000000000000
χ2922-2-22-222-2-2-222-2000000002i−2i−2i2i0000000022-2-22-222-2-2-222-2000000002i−2i−2i2i00000000
χ3022-2-22-222-2-2-222-200000000−2i2i2i−2i0000000022-2-22-222-2-2-222-200000000−2i2i2i−2i00000000
χ3144444-4-4-4-4000000000000000000000000044444-4-4-4-40000000000000000000000000
χ3244-4-444-4-44000000000000000000000000044-4-444-4-440000000000000000000000000
χ338-8000000042−42000000000000000000000008-8000000042−4200000000000000000000000
χ348-80000000−4242000000000000000000000008-80000000−424200000000000000000000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ37111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ38111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ3911111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ4011111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ4211111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ43222222222-2-2-2-2-222-2-20000000000000000-2-2-2-2-2-2-2-2-222222-2-2220000000000000000
χ44222222222-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-2-22222222-2-20000000000000000
χ45222-2-222-2-200000002i−2i22−2−2i2i2−i2−i200000000-2-2-222-2-2220000000−2i2i−2−222−i2−i2i2i200000000
χ46222-2-222-2-200000002i−2i−2−222−i2−i2i2i200000000-2-2-222-2-2220000000−2i2i22−2−2i2i2−i2−i200000000
χ47222-2-222-2-20000000−2i2i22−2−2−i2−i2i2i200000000-2-2-222-2-22200000002i−2i−2−222i2i2−i2−i200000000
χ48222-2-222-2-20000000−2i2i−2−222i2i2−i2−i200000000-2-2-222-2-22200000002i−2i22−2−2−i2−i2i2i200000000
χ49222-2-2-2-222222-2-200000000000000002-200-2-2-22222-2-2-2-2-2220000000000000000-2200
χ50222-2-2-2-222222-2-20000000000000000-2200-2-2-22222-2-2-2-2-22200000000000000002-200
χ51222-2-2-2-222-2-2-2220000000000002-2000000-2-2-22222-2-2222-2-2000000000000-22000000
χ52222-2-2-2-222-2-2-222000000000000-22000000-2-2-22222-2-2222-2-20000000000002-2000000
χ5322-22-22-22-222-22-20000000000000000002i−2i-2-22-22-22-22-2-22-22000000000000000000−2i2i
χ5422-22-22-22-222-22-2000000000000000000−2i2i-2-22-22-22-22-2-22-220000000000000000002i−2i
χ5522-22-22-22-2-2-22-22000000000000002i−2i0000-2-22-22-22-2222-22-200000000000000−2i2i0000
χ5622-22-22-22-2-2-22-2200000000000000−2i2i0000-2-22-22-22-2222-22-2000000000000002i−2i0000
χ5722-22-2-22-22000002-2002−22−22−22−200000000-2-22-222-22-200000-2200−22−22−22−2200000000
χ5822-22-2-22-22000002-200−22−22−22−2200000000-2-22-222-22-200000-22002−22−22−22−200000000
χ5922-22-2-22-2200000-22002−22−2−22−2200000000-2-22-222-22-2000002-200−22−222−22−200000000
χ6022-22-2-22-2200000-2200−22−222−22−200000000-2-22-222-22-2000002-2002−22−2−22−2200000000
χ6122-2-22-222-222-2-2200002-2-22000000000000-2-222-22-2-22-2-222-20000-222-2000000000000
χ6222-2-22-222-222-2-220000-222-2000000000000-2-222-22-2-22-2-222-200002-2-22000000000000
χ6322-2-22-222-2-2-222-2000000002i−2i−2i2i00000000-2-222-22-2-2222-2-2200000000−2i2i2i−2i00000000
χ6422-2-22-222-2-2-222-200000000−2i2i2i−2i00000000-2-222-22-2-2222-2-22000000002i−2i−2i2i00000000
χ6544444-4-4-4-40000000000000000000000000-4-4-4-4-444440000000000000000000000000
χ6644-4-444-4-440000000000000000000000000-4-444-4-444-40000000000000000000000000
χ678-8000000042−4200000000000000000000000-880000000−424200000000000000000000000
χ688-80000000−424200000000000000000000000-88000000042−4200000000000000000000000

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