Finite Group Databasebeta

← Group #491397

Character table — Group #491397

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122244444444888824488888824448888161616161616161616161616161616168888444488
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
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-111
χ91111-1-1-1-111111111-11-111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ101111-1-1-1-111111111-11-111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-11
χ111111-1-1-1-111111111-11-111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1111111-1-11-1-11-11
χ121111-1-1-1-111111111-11-111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-111-111-11-1
χ131111-1-1-1-111111111-11-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1
χ141111-1-1-1-111111111-11-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-1-11
χ151111-1-1-1-111111111-11-111-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-111-1-1-111-1-11
χ161111-1-1-1-111111111-11-111-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1111-1-111-1
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
χ1922222222-2-2220000-2-2-20000002-22-200002−22−22−22−222−2−222−2−20000000000
χ2022222222-2-2220000-2-2-20000002-22-20000−22−22−22−22−2−222−2−2220000000000
χ2122222222-2-2220000-2-2-2000000-22-2200002−22−22−22−2−2−222−2−2220000000000
χ2222222222-2-2220000-2-2-2000000-22-220000−22−22−22−2222−2−222−2−20000000000
χ23222222-2-222-2-222222-2-2-2-222-2-20000000022-2-2-2-222000000000000000000
χ24222222-2-222-2-222222-2-2-2-222-2-200000000-2-22222-2-2000000000000000000
χ25222222-2-222-2-2-2-2-2-22-2-222-2-22200000000000000002i−2i2i−2i2i−2i2i−2i0000000000
χ26222222-2-222-2-2-2-2-2-22-2-222-2-2220000000000000000−2i2i−2i2i−2i2i−2i2i0000000000
χ27222222-2-2-2-2-2-20000-22200000000002i−2i2i−2i2−2−22−222−2i2−i2−i2i2i2−i2−i2i20000000000
χ28222222-2-2-2-2-2-20000-22200000000002i−2i2i−2i−222−22−2−22−i2i2i2−i2−i2i2i2−i20000000000
χ29222222-2-2-2-2-2-20000-2220000000000−2i2i−2i2i2−2−22−222−2−i2i2i2−i2−i2i2i2−i20000000000
χ30222222-2-2-2-2-2-20000-2220000000000−2i2i−2i2i−222−22−2−22i2−i2−i2i2i2−i2−i2i20000000000
χ312222-2-22222-2-22222-2-22-2-2-2-222000000002222-2-2-2-2000000000000000000
χ322222-2-22222-2-22222-2-22-2-2-2-22200000000-2-2-2-22222000000000000000000
χ332222-2-22222-2-2-2-2-2-2-2-222222-2-200000000000000002i−2i2i−2i−2i2i−2i2i0000000000
χ342222-2-22222-2-2-2-2-2-2-2-222222-2-20000000000000000−2i2i−2i2i2i−2i2i−2i0000000000
χ352222-2-222-2-2-2-2000022-200000000002i−2i−2i2i2−22−2−22−22i2−i2−i2i2−i2i2i2−i20000000000
χ362222-2-222-2-2-2-2000022-200000000002i−2i−2i2i−22−222−22−2−i2i2i2−i2i2−i2−i2i20000000000
χ372222-2-222-2-2-2-2000022-20000000000−2i2i2i−2i2−22−2−22−22−i2i2i2−i2i2−i2−i2i20000000000
χ382222-2-222-2-2-2-2000022-20000000000−2i2i2i−2i−22−222−22−2i2−i2−i2i2−i2i2i2−i20000000000
χ392222-2-2-2-22222-2-2-2-2-22-2-2-2222222-2-2-2-22200000000000000000000000000
χ402222-2-2-2-22222-2-2-2-2-22-2-2-22222-2-22222-2-200000000000000000000000000
χ412222-2-2-2-2-2-22200002-220000002-2-2200002−2−222−2−2222−2−2−2−2220000000000
χ422222-2-2-2-2-2-22200002-220000002-2-220000−222−2−222−2−2−22222−2−20000000000
χ432222-2-2-2-2-2-22200002-22000000-222-200002−2−222−2−22−2−22222−2−20000000000
χ442222-2-2-2-2-2-22200002-22000000-222-20000−222−2−222−222−2−2−2−2220000000000
χ4544-4-400004-40044-4-400000000000000000000000000000000022−2200000000
χ4644-4-400004-40044-4-4000000000000000000000000000000000−222200000000
χ4744-4-400004-400-4-444000000000000000000000000000000000002i2−2i2000000
χ4844-4-400004-400-4-44400000000000000000000000000000000000−2i22i2000000
χ494-4-444i−4i4i−4i004-422−2222−2200022−222i2−2i22i2−2i20000000000000000000000000000000000
χ504-4-444i−4i4i−4i004-4−2222−2222000−2222−2i22i2−2i22i20000000000000000000000000000000000
χ514-4-444i−4i−4i4i00-4422−2222−22000−22222i2−2i2−2i22i20000000000000000000000000000000000
χ524-4-444i−4i−4i4i00-44−2222−222200022−22−2i22i22i2−2i20000000000000000000000000000000000
χ534-4-44−4i4i4i−4i00-4422−2222−22000−2222−2i22i22i2−2i20000000000000000000000000000000000
χ544-4-44−4i4i4i−4i00-44−2222−222200022−222i2−2i2−2i22i20000000000000000000000000000000000
χ554-4-44−4i4i−4i4i004-422−2222−2200022−22−2i22i2−2i22i20000000000000000000000000000000000
χ564-4-44−4i4i−4i4i004-4−2222−2222000−22222i2−2i22i2−2i20000000000000000000000000000000000
χ5788-8-80000-880000000000000000000000000000000000000000000000000
χ588-88-80000000042−42−42420000000000000000000000000000000000000000000
χ598-88-800000000−424242−420000000000000000000000000000000000000000000

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