Finite Group Databasebeta

← Group #141338

Character table — Group #141338

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order1222444444444488882488888888888888888888888888888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-11111-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111-1-11111-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111-1-11111-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111-1-11111-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000
χ1922222222-2-2-2-2-2-200002-200000022-2-222-2-20000000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222222-2-2-2-2-2-200002-200000022-2-222-2-20000000000000000−i2i2−i2i2−i2i2−i2i20000
χ2122222222-2-2-2-2-2-200002-2000000-2-222-2-2220000000000000000i2−i2i2−i2−i2i2−i2i20000
χ2222222222-2-2-2-2-2-200002-2000000-2-222-2-2220000000000000000−i2i2−i2i2i2−i2i2−i20000
χ23222222-2-22222-2-22222-2-222-2-2-2-2000000000000000000002-22-2000000000000
χ24222222-2-22222-2-22222-2-222-2-2-2-200000000000000000000-22-22000000000000
χ25222222-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000002i−2i2i−2i0000000000000000
χ26222222-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000−2i2i−2i2i0000000000000000
χ272222-2-22222-2-2-2-22222-22-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000
χ282222-2-22222-2-2-2-22222-22-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000
χ292222-2-222-2-222220000-2-200000022-2-2-2-22200000000000000002−2−222−2−220000
χ302222-2-222-2-222220000-2-200000022-2-2-2-2220000000000000000−222−2−222−20000
χ312222-2-222-2-222220000-2-2000000-2-22222-2-200000000000000002−2−22−222−20000
χ322222-2-222-2-222220000-2-2000000-2-22222-2-20000000000000000−222−22−2−220000
χ332222-2-2-2-222-2-22222222-2-2-222-2-200000000000000002-2-220000000000000000
χ342222-2-2-2-222-2-22222222-2-2-222-2-20000000000000000-222-20000000000000000
χ352222-2-2-2-222-2-222-2-2-2-22-222-2-222000000000000000000002i−2i−2i2i000000000000
χ362222-2-2-2-222-2-222-2-2-2-22-222-2-22200000000000000000000−2i2i2i−2i000000000000
χ37444444-4-4-4-4-4-4440000-44000000000000000000000000000000000000000000
χ384444-4-4-4-4-4-444-4-4000044000000000000000000000000000000000000000000
χ3944-4-4004-40000002222−22−2200000022−2200004-4002222−22−22000000000000000000000000
χ4044-4-4004-40000002222−22−2200000022−220000-4400−22−222222000000000000000000000000
χ4144-4-4004-4000000−22−222222000000−222200004-400−22−222222000000000000000000000000
χ4244-4-4004-4000000−22−222222000000−22220000-44002222−22−22000000000000000000000000
χ4344-4-400-440000002222−22−22000000−2222004-4000000002222−22−2200000000000000000000
χ4444-4-400-440000002222−22−22000000−222200-4400000000−22−22222200000000000000000000
χ4544-4-400-44000000−22−22222200000022−22004-400000000−22−22222200000000000000000000
χ4644-4-400-44000000−22−22222200000022−2200-44000000002222−22−2200000000000000000000
χ474-44-4000000004i−4i2i2−2i22i2−2i2000022−22002i2−2i2000022−222i−2i2i−2i2-22-200000000000000000000
χ484-44-4000000004i−4i2i2−2i22i2−2i2000022−2200−2i22i20000−2222−2i2i−2i2i-22-2200000000000000000000
χ494-44-4000000004i−4i−2i22i2−2i22i20000−2222002i2−2i2000022−22−2i2i−2i2i-22-2200000000000000000000
χ504-44-4000000004i−4i−2i22i2−2i22i20000−222200−2i22i20000−22222i−2i2i−2i2-22-200000000000000000000
χ514-44-400000000−4i4i2i2−2i22i2−2i20000−2222002i2−2i20000−2222−2i2i−2i2i2-22-200000000000000000000
χ524-44-400000000−4i4i2i2−2i22i2−2i20000−222200−2i22i2000022−222i−2i2i−2i-22-2200000000000000000000
χ534-44-400000000−4i4i−2i22i2−2i22i2000022−22002i2−2i20000−22222i−2i2i−2i-22-2200000000000000000000
χ544-44-400000000−4i4i−2i22i2−2i22i2000022−2200−2i22i2000022−22−2i2i−2i2i2-22-200000000000000000000
χ554-4-444i−4i004-44i−4i00000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000
χ564-4-444i−4i004-44i−4i0000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000
χ574-4-444i−4i00-44−4i4i004i−4i−4i4i004-40000000000000000000000000000000000000000
χ584-4-444i−4i00-44−4i4i00−4i4i4i−4i00-440000000000000000000000000000000000000000
χ594-4-44−4i4i004-4−4i4i00000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000
χ604-4-44−4i4i004-4−4i4i0000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000
χ614-4-44−4i4i00-444i−4i004i−4i−4i4i00-440000000000000000000000000000000000000000
χ624-4-44−4i4i00-444i−4i00−4i4i4i−4i004-40000000000000000000000000000000000000000

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