Finite Group Databasebeta

← Group #491296

Character table — Group #491296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122244444444888824488888844448888161616161616161616161616161616168888244488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ91111-1-1-1-111111111-11-1-1-111-1-11-11-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111-1-1-1-111111111-11-1-1-111-1-11-11-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11
χ111111-1-1-1-111111111-11-1-1-111-1-11-11-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-11
χ121111-1-1-1-111111111-11-1-1-111-1-11-11-111-1-1-1-1-1-11111-1-1-1-11111-1-111-111-11-1
χ131111-1-1-1-111111111-11-1-1-111-1-1-11-11-1-1111111-1-1-1-1-1-1-1-1111111-1-1-111-1-11
χ141111-1-1-1-111111111-11-1-1-111-1-1-11-11-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-111-1
χ151111-1-1-1-111111111-11-1-1-111-1-1-11-11-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1111-1
χ161111-1-1-1-111111111-11-1-1-111-1-1-11-11-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ17222222222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ1922222222-2-2220000-2-2-20000002-2-22000022−2−222−2−222−2−222−2−20000000000
χ2022222222-2-2220000-2-2-20000002-2-220000−2−222−2−222−2−222−2−2220000000000
χ2122222222-2-2220000-2-2-2000000-222-2000022−2−222−2−2−2−222−2−2220000000000
χ2222222222-2-2220000-2-2-2000000-222-20000−2−222−2−22222−2−222−2−20000000000
χ23222222-2-222-2-22222-2-22-2-2-2-22200000000000000002-22-22-22-20000000000
χ24222222-2-222-2-22222-2-22-2-2-2-2220000000000000000-22-22-22-220000000000
χ25222222-2-222-2-2-2-2-2-2-2-222222-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ26222222-2-222-2-2-2-2-2-2-2-222222-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ27222222-2-2-2-2-2-2000022-200000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000
χ28222222-2-2-2-2-2-2000022-200000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000
χ29222222-2-2-2-2-2-2000022-20000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000
χ30222222-2-2-2-2-2-2000022-20000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000
χ312222-2-22222-2-222222-2-222-2-2-2-200000000000000002-22-2-22-220000000000
χ322222-2-22222-2-222222-2-222-2-2-2-20000000000000000-22-222-22-20000000000
χ332222-2-22222-2-2-2-2-2-22-2-2-2-22222000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ342222-2-22222-2-2-2-2-2-22-2-2-2-2222200000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ352222-2-222-2-2-2-20000-22200000000002i−2i−2i2ii2−i2−i2i2−i2i2i2−i22−2−22−222−20000000000
χ362222-2-222-2-2-2-20000-22200000000002i−2i−2i2i−i2i2i2−i2i2−i2−i2i2−222−22−2−220000000000
χ372222-2-222-2-2-2-20000-2220000000000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000
χ382222-2-222-2-2-2-20000-2220000000000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000
χ392222-2-2-2-22222-2-2-2-2-22-222-2-2222-22-2-2-22200000000000000000000000000
χ402222-2-2-2-22222-2-2-2-2-22-222-2-222-22-2222-2-200000000000000000000000000
χ412222-2-2-2-2-2-22200002-2200000022-2-2000022−2−2−2−22222−2−2−2−2220000000000
χ422222-2-2-2-2-2-22200002-2200000022-2-20000−2−22222−2−2−2−22222−2−20000000000
χ432222-2-2-2-2-2-22200002-22000000-2-222000022−2−2−2−222−2−22222−2−20000000000
χ442222-2-2-2-2-2-22200002-22000000-2-2220000−2−22222−2−222−2−2−2−2220000000000
χ454-44-44i−4i4i−4i004-42222−22−220002i2−2i222−222i2−2i20000000000000000000000000000000000
χ464-44-44i−4i4i−4i004-4−22−222222000−2i22i2−2222−2i22i20000000000000000000000000000000000
χ474-44-44i−4i−4i4i00-442222−22−22000−2i22i2−22222i2−2i20000000000000000000000000000000000
χ484-44-44i−4i−4i4i00-44−22−2222220002i2−2i222−22−2i22i20000000000000000000000000000000000
χ494-44-4−4i4i4i−4i00-442222−22−220002i2−2i2−2222−2i22i20000000000000000000000000000000000
χ504-44-4−4i4i4i−4i00-44−22−222222000−2i22i222−222i2−2i20000000000000000000000000000000000
χ514-44-4−4i4i−4i4i004-42222−22−22000−2i22i222−22−2i22i20000000000000000000000000000000000
χ524-44-4−4i4i−4i4i004-4−22−2222220002i2−2i2−22222i2−2i20000000000000000000000000000000000
χ534-4-4400004-4004-44-40000000000000000000000000000000002i2−2i200000000
χ544-4-4400004-4004-44-4000000000000000000000000000000000−2i22i200000000
χ554-4-4400004-400-44-44000000000000000000000000000000000002i2−2i2000000
χ564-4-4400004-400-44-4400000000000000000000000000000000000−2i22i2000000
χ5788-8-80000000042−42−42420000000000000000000000000000000000000000000
χ5888-8-800000000−424242−420000000000000000000000000000000000000000000
χ598-8-880000-880000000000000000000000000000000000000000000000000

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