Finite Group Databasebeta

← Group #135133

Character table — Group #135133

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order1222444444888888882444888888888888888888882244888816161616161616168888
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
χ51111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-11111-11111-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1-1-11-11-111-1-1ii−i−iii−i−ii−ii−i
χ101111-11111-11111-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1-1-11-11-111-1-1−i−iii−i−iii−ii−ii
χ111111-11111-11111-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1-11-11-1-111ii−i−iii−i−i−ii−ii
χ121111-11111-11111-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1-11-11-1-111−i−iii−i−iiii−ii−i
χ131111-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111-11-1-1-111ii−i−i−i−iiii−i−ii
χ141111-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111-11-1-1-111−i−iiiii−i−i−iii−i
χ151111-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-11-1111-1-1ii−i−i−i−iii−iii−i
χ161111-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-11-1111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000000000000000
χ182222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000
χ192222222-2-2200002222-2-22-222-2-2-2-20000000000000022-2-20000000000000000
χ202222222-2-2200002222-2-22-222-2-2-2-200000000000000-2-2220000000000000000
χ212222222-2-220000-2-2-2-2-2-22-2-2-222220000000000000000002i−2i2i−2i000000000000
χ222222222-2-220000-2-2-2-2-2-22-2-2-22222000000000000000000−2i2i−2i2i000000000000
χ2322222-2-222222220000-22-2-2000000-2-222-2-200000000000000002−22−22−22−20000
χ2422222-2-222222220000-22-2-2000000-2-222-2-20000000000000000−22−22−22−220000
χ2522222-2-2222-2-2-2-20000-22-2-200000022-2-22200000000000000002−22−2−22−220000
χ2622222-2-2222-2-2-2-20000-22-2-200000022-2-2220000000000000000−22−222−22−20000
χ272222-22222-222222222-2-2-22-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000
χ282222-22222-2-2-2-2-22222-2-2-22-2-2-2-222-2-222222222-2-2-2-200000000000000000000
χ292222-222-2-2-20000222222-2-2-2-222-2-20000000000000000002i−2i−2i2i000000000000
χ302222-222-2-2-20000222222-2-2-2-222-2-2000000000000000000−2i2i2i−2i000000000000
χ312222-222-2-2-20000-2-2-2-222-2-222-2-222000000000000002-2-220000000000000000
χ322222-222-2-2-20000-2-2-2-222-2-222-2-22200000000000000-222-20000000000000000
χ332222-2-2-222-2222200002-22-2000000-2-2-2-2220000000000000000i2−i2−i2i2i2−i2−i2i20000
χ342222-2-2-222-2222200002-22-2000000-2-2-2-2220000000000000000−i2i2i2−i2−i2i2i2−i20000
χ352222-2-2-222-2-2-2-2-200002-22-20000002222-2-20000000000000000i2−i2−i2i2−i2i2i2−i20000
χ362222-2-2-222-2-2-2-2-200002-22-20000002222-2-20000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3744444-4-4-4-44000000004-4-440000000000000000000000000000000000000000
χ384444-4-4-4-4-4-400000000-44440000000000000000000000000000000000000000
χ3944-4-404-40002i22i2−2i2−2i200000000004i−4i002i2−2i200002222−22−22000000000000000000000000
χ4044-4-404-40002i22i2−2i2−2i20000000000−4i4i002i2−2i20000−22−222222000000000000000000000000
χ4144-4-404-4000−2i2−2i22i22i200000000004i−4i00−2i22i20000−22−222222000000000000000000000000
χ4244-4-404-4000−2i2−2i22i22i20000000000−4i4i00−2i22i200002222−22−22000000000000000000000000
χ4344-4-40-440002i22i2−2i2−2i244-4-40000000000−2i22i2000000002i22i2−2i2−2i200000000000000000000
χ4444-4-40-440002i22i2−2i2−2i2-4-4440000000000−2i22i200000000−2i2−2i22i22i200000000000000000000
χ4544-4-40-44000−2i2−2i22i22i244-4-400000000002i2−2i200000000−2i2−2i22i22i200000000000000000000
χ4644-4-40-44000−2i2−2i22i22i2-4-44400000000002i2−2i2000000002i22i2−2i2−2i200000000000000000000
χ474-44-440000-422−2222−2222−2222−22000022−2200000022−22002-22-22-22-200000000000000000000
χ484-44-440000-422−2222−22−2222−22220000−222200000022−2200-22-22-22-2200000000000000000000
χ494-44-440000-4−2222−222222−2222−22000022−22000000−222200-22-22-22-2200000000000000000000
χ504-44-440000-4−2222−2222−2222−22220000−2222000000−2222002-22-22-22-200000000000000000000
χ514-44-4-40000422−2222−2222−2222−220000−2222000000−222200-22-222-22-200000000000000000000
χ524-44-4-40000422−2222−22−2222−2222000022−22000000−2222002-22-2-22-2200000000000000000000
χ534-44-4-400004−2222−222222−2222−220000−222200000022−22002-22-2-22-2200000000000000000000
χ544-44-4-400004−2222−2222−2222−2222000022−2200000022−2200-22-222-22-200000000000000000000
χ554-4-440004-404i−4i−4i4i22−22−22220000000022−2200000000002i2−2i2−2i22i200000000000000000000
χ564-4-440004-404i−4i−4i4i−222222−2200000000−22220000000000−2i22i22i2−2i200000000000000000000
χ574-4-440004-40−4i4i4i−4i22−22−22220000000022−220000000000−2i22i22i2−2i200000000000000000000
χ584-4-440004-40−4i4i4i−4i−222222−2200000000−222200000000002i2−2i2−2i22i200000000000000000000
χ594-4-44000-440000022−22−222200000000−222200004-422−22−2222000000000000000000000000
χ604-4-44000-440000022−22−222200000000−22220000-44−222222−22000000000000000000000000
χ614-4-44000-4400000−222222−220000000022−2200004-4−222222−22000000000000000000000000
χ624-4-44000-4400000−222222−220000000022−220000-4422−22−2222000000000000000000000000

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