Finite Group Databasebeta

← Group #401005

Character table — Group #401005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12222222224444444488888888888822224444444488888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ172222222222-2-2-2-2-2-2-2-2000000000000000022-2-20000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ182222222222-2-2-2-2-2-2-2-2000000000000000022-2-2000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222222-2-2-2-2-2-2-2-20000000000000000-2-2220000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222222222-2-2-2-2-2-2-2-20000000000000000-2-222000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ21222222-2-2-2-22222-2-2-2-200002i2i2i2i−2i−2i−2i−2i0022000000-2-2002i−2i2i−2i00000000000000000000
χ22222222-2-2-2-22222-2-2-2-200002i2i2i2i−2i−2i−2i−2i00-2-20000002200−2i2i−2i2i00000000000000000000
χ23222222-2-2-2-22222-2-2-2-20000−2i−2i−2i−2i2i2i2i2i0022000000-2-200−2i2i−2i2i00000000000000000000
χ24222222-2-2-2-22222-2-2-2-20000−2i−2i−2i−2i2i2i2i2i00-2-200000022002i−2i2i−2i00000000000000000000
χ25222222-2-2-2-2-2-2-2-2222222-2-2000000002-20000002-2002-22-2-2200000000000000000000
χ26222222-2-2-2-2-2-2-2-2222222-2-200000000-22000000-22002-2-222-200000000000000000000
χ27222222-2-2-2-2-2-2-2-22222-2-222000000002-20000002-200-22-222-200000000000000000000
χ28222222-2-2-2-2-2-2-2-22222-2-22200000000-22000000-2200-222-2-2200000000000000000000
χ292222-2-222-2-222-2-222-2-200002i2i−2i−2i2i2i−2i−2i22000000-2-2000000002i−2i2i−2i0000000000000000
χ302222-2-222-2-222-2-222-2-200002i2i−2i−2i2i2i−2i−2i-2-20000002200000000−2i2i−2i2i0000000000000000
χ312222-2-222-2-222-2-222-2-20000−2i−2i2i2i−2i−2i2i2i22000000-2-200000000−2i2i−2i2i0000000000000000
χ322222-2-222-2-222-2-222-2-20000−2i−2i2i2i−2i−2i2i2i-2-200000022000000002i−2i2i−2i0000000000000000
χ332222-2-222-2-2-2-222-2-22222-2-200000000002-20000002-2-2200002-2-220000000000000000
χ342222-2-222-2-2-2-222-2-22222-2-20000000000-22000000-22-220000-222-20000000000000000
χ352222-2-222-2-2-2-222-2-222-2-22200000000002-20000002-22-20000-222-20000000000000000
χ362222-2-222-2-2-2-222-2-222-2-2220000000000-22000000-222-200002-2-220000000000000000
χ372222-2-2-2-22222-2-2-2-222222222-2-2-2-22200002-22-20000-2-2000000000000000000000000
χ382222-2-2-2-22222-2-2-2-2222222-2-22222-2-20000-22-220000-2-2000000000000000000000000
χ392222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-2220000-22-22000022000000000000000000000000
χ402222-2-2-2-22222-2-2-2-222-2-2-2-2-2-22222-2-200002-22-2000022000000000000000000000000
χ412222-2-2-2-222-2-22222-2-20000000000002-22-22-2-22-22-2200000000000000000000000000
χ422222-2-2-2-222-2-22222-2-20000000000002-2-22-222-2-222-200000000000000000000000000
χ432222-2-2-2-222-2-22222-2-2000000000000-222-2-222-22-2-2200000000000000000000000000
χ442222-2-2-2-222-2-22222-2-2000000000000-22-222-2-222-22-200000000000000000000000000
χ452-2-222-22-22-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000002-2002i−2i00000000
χ462-2-222-22-22-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000-2200−2i2i00000000
χ472-2-222-22-22-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-200−2i2i00000000
χ482-2-222-22-22-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000-22002i−2i00000000
χ492-2-222-2-22-222-22-2-22-2200002-22-2-22-220000000000000000000000000000002-2002-200
χ502-2-222-2-22-222-22-2-22-2200002-22-2-22-22000000000000000000000000000000-2200-2200
χ512-2-222-2-22-222-22-2-22-220000-22-222-22-20000000000000000000000000000002-200-2200
χ522-2-222-2-22-222-22-2-22-220000-22-222-22-2000000000000000000000000000000-22002-200
χ532-2-22-222-2-222-2-222-2-2200002-2-222-2-22000000000000000000000000000000002-2002-2
χ542-2-22-222-2-222-2-222-2-2200002-2-222-2-2200000000000000000000000000000000-2200-22
χ552-2-22-222-2-222-2-222-2-220000-222-2-222-2000000000000000000000000000000002-200-22
χ562-2-22-222-2-222-2-222-2-220000-222-2-222-200000000000000000000000000000000-22002-2
χ572-2-22-22-222-22-2-22-222-200002i−2i−2i2i−2i2i2i−2i00000000000000000000002-2002i−2i0000000000
χ582-2-22-22-222-22-2-22-222-200002i−2i−2i2i−2i2i2i−2i0000000000000000000000-2200−2i2i0000000000
χ592-2-22-22-222-22-2-22-222-20000−2i2i2i−2i2i−2i−2i2i00000000000000000000002-200−2i2i0000000000
χ602-2-22-22-222-22-2-22-222-20000−2i2i2i−2i2i−2i−2i2i0000000000000000000000-22002i−2i0000000000
χ614-4-444-44-44-4-44-44-44-4400000000000000000000000000000000000000000000000000
χ624-4-444-4-44-44-44-444-44-400000000000000000000000000000000000000000000000000
χ634-4-44-444-4-44-444-4-444-400000000000000000000000000000000000000000000000000
χ644-4-44-44-444-4-444-44-4-4400000000000000000000000000000000000000000000000000
χ6588-8-800000000000000004i2−4i20000000000000000000000000000000000000000000000
χ6688-8-80000000000000000−4i24i20000000000000000000000000000000000000000000000
χ678-88-8000000000000004i2−4i2000000000000000000000000000000000000000000000000
χ688-88-800000000000000−4i24i2000000000000000000000000000000000000000000000000

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