Finite Group Databasebeta

← Group #240798

Character table — Group #240798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222444444444444442444448888888888888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-111-1-1-1-1-1-1-1-1111111-1111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ101111-1-111-1-1-1-1-1-1-1-1111111-1111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ111111-1-111-1-1-1-1-1-1-1-1111111-1111-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111-11-1-1-11111-1-1-1-111
χ121111-1-111-1-1-1-1-1-1-1-1111111-1111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ131111-1-111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111-11-111-1-1-1-111-1-111
χ141111-1-111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-11-11-1-11111-1-111-1-1
χ151111-1-111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11-11-1-1-111-1-11111-1-1
χ161111-1-111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-11-1111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-2-2-2222-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ18222222222222-2-2-2-2-2-2-2-2-2-2222-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ1922222222-2-2-2-222222-2-2-2-222-2-22-2-200000000000000000000000000002-22-200000000
χ2022222222-2-2-2-222222-2-2-2-222-2-22-2-20000000000000000000000000000-22-2200000000
χ2122222222-2-2-2-2-2-2-2-2-22222-22-2-2-22222-2-222-2-200000000000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-22222-22-2-2-222-2-222-2-22200000000000000000000000000000000
χ23222222-2-222-2-222-2-2222-2-22-22-2-22-2000000002222-2-2-2-2000000000000000000000000
χ24222222-2-222-2-222-2-2222-2-22-22-2-22-200000000-2-2-2-22222000000000000000000000000
χ25222222-2-222-2-2-2-222-2-2-222-2-22-22-22000000000000000000000000000000002i−2i2i−2i0000
χ26222222-2-222-2-2-2-222-2-2-222-2-22-22-2200000000000000000000000000000000−2i2i−2i2i0000
χ27222222-2-2-2-22222-2-22-2-2222-2-22-2-2200000000000000000000000022-2-2000000000000
χ28222222-2-2-2-22222-2-22-2-2222-2-22-2-22000000000000000000000000-2-222000000000000
χ29222222-2-2-2-222-2-222-222-2-2-2-2-2222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ30222222-2-2-2-222-2-222-222-2-2-2-2-2222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312222-2-22222222222-22222-2-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ322222-2-22222222222-22222-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ332222-2-2222222-2-2-2-22-2-2-2-22-2-2-222200000000000000000000000000002-2-2200000000
χ342222-2-2222222-2-2-2-22-2-2-2-22-2-2-22220000000000000000000000000000-222-200000000
χ352222-2-222-2-2-2-22222-2-2-2-2-2-2-222-2220000000000000000000000000000000000002i−2i−2i2i
χ362222-2-222-2-2-2-22222-2-2-2-2-2-2-222-222000000000000000000000000000000000000−2i2i2i−2i
χ372222-2-2-2-222-2-222-2-2-222-2-2-22-222-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ382222-2-2-2-222-2-222-2-2-222-2-2-22-222-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ392222-2-2-2-222-2-2-2-2222-2-22222-22-22-20000000000000000000000002-2-22000000000000
χ402222-2-2-2-222-2-2-2-2222-2-22222-22-22-2000000000000000000000000-222-2000000000000
χ412222-2-2-2-2-2-22222-2-2-2-2-222-222-222-2000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-22222-2-2-2-2-222-222-222-200000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-222-2-222222-2-2222-2-2-220000000022-2-2-2-222000000000000000000000000
χ442222-2-2-2-2-2-222-2-222222-2-2222-2-2-2200000000-2-22222-2-2000000000000000000000000
χ452-22-2002-22i−2i2i−2i2i−2i2i−2i02-22-20000000002i−2i2-200i2−i22−2i2−i22−22−22−2i2−i2i2−i20000000000000000
χ462-22-2002-22i−2i2i−2i2i−2i2i−2i02-22-20000000002i−2i2-200−i2i2−22−i2i2−22−22−22−i2i2−i2i20000000000000000
χ472-22-2002-22i−2i2i−2i2i−2i2i−2i02-22-2000000000−2i2i-2200i2−i22−2i2−i22−2−22−22−i2i2−i2i20000000000000000
χ482-22-2002-22i−2i2i−2i2i−2i2i−2i02-22-2000000000−2i2i-2200−i2i2−22−i2i2−222−22−2i2−i2i2−i20000000000000000
χ492-22-2002-2−2i2i−2i2i−2i2i−2i2i02-22-20000000002i−2i-2200i2−i2−22i2−i2−222−22−2−i2i2−i2i20000000000000000
χ502-22-2002-2−2i2i−2i2i−2i2i−2i2i02-22-20000000002i−2i-2200−i2i22−2−i2i22−2−22−22i2−i2i2−i20000000000000000
χ512-22-2002-2−2i2i−2i2i−2i2i−2i2i02-22-2000000000−2i2i2-200i2−i2−22i2−i2−22−22−22i2−i2i2−i20000000000000000
χ522-22-2002-2−2i2i−2i2i−2i2i−2i2i02-22-2000000000−2i2i2-200−i2i22−2−i2i22−22−22−2−i2i2−i2i20000000000000000
χ532-22-200-222i−2i−2i2i2i−2i−2i2i02-2-2200000002-200002i−2ii2−i22−2−i2i2−22i2−i2−i2i22−2−220000000000000000
χ542-22-200-222i−2i−2i2i2i−2i−2i2i02-2-2200000002-200002i−2i−i2i2−22i2−i22−2−i2i2i2−i2−222−20000000000000000
χ552-22-200-222i−2i−2i2i2i−2i−2i2i02-2-220000000-220000−2i2ii2−i22−2−i2i2−22−i2i2i2−i2−222−20000000000000000
χ562-22-200-222i−2i−2i2i2i−2i−2i2i02-2-220000000-220000−2i2i−i2i2−22i2−i22−2i2−i2−i2i22−2−220000000000000000
χ572-22-200-22−2i2i2i−2i−2i2i2i−2i02-2-2200000002-20000−2i2ii2−i2−22−i2i22−2i2−i2−i2i2−222−20000000000000000
χ582-22-200-22−2i2i2i−2i−2i2i2i−2i02-2-2200000002-20000−2i2i−i2i22−2i2−i2−22−i2i2i2−i22−2−220000000000000000
χ592-22-200-22−2i2i2i−2i−2i2i2i−2i02-2-220000000-2200002i−2ii2−i2−22−i2i22−2−i2i2i2−i22−2−220000000000000000
χ602-22-200-22−2i2i2i−2i−2i2i2i−2i02-2-220000000-2200002i−2i−i2i22−2i2−i2−22i2−i2−i2i2−222−20000000000000000
χ614-44-4004-44i−4i4i−4i−4i4i−4i4i0-44-4400000000000000000000000000000000000000000000000
χ624-44-4004-4−4i4i−4i4i4i−4i4i−4i0-44-4400000000000000000000000000000000000000000000000
χ634-44-400-444i−4i−4i4i−4i4i4i−4i0-444-400000000000000000000000000000000000000000000000
χ644-44-400-44−4i4i4i−4i4i−4i−4i4i0-444-400000000000000000000000000000000000000000000000
χ6588-8-88-800000000000000000000000000000000000000000000000000000000000000
χ6688-8-8-8800000000000000000000000000000000000000000000000000000000000000
χ678-8-8800000000000080000-80000000000000000000000000000000000000000000000
χ688-8-88000000000000-8000080000000000000000000000000000000000000000000000

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