Finite Group Databasebeta

← Group #145973

Character table — Group #145973

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order12222244444488884448888444488888161616161616161688888888161616164488
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ511111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ9222222222222-2-2-2-2222-2-2-2-22222-2-2-2-2-2000000000000000000000000
χ10222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1122222222-222-22222-2-2-222-2-20000-200002222-2-2-2-20000000000000000
χ1222222222-222-22222-2-2-222-2-20000-20000-2-2-2-222220000000000000000
χ1322222222-222-2-2-2-2-2-2-2-2-2-22200002000000000000000000002i2i−2i−2i0000
χ1422222222-222-2-2-2-2-2-2-2-2-2-2220000200000000000000000000−2i−2i2i2i0000
χ152222-2-2222-2-2222222-2-2-2-2220000-200000000000022-2-2000000000000
χ162222-2-2222-2-2222222-2-2-2-2220000-2000000000000-2-222000000000000
χ172222-2-2222-2-22-2-2-2-22-2-222-2-200002000000000000000000000000002i−2i
χ182222-2-2222-2-22-2-2-2-22-2-222-2-20000200000000000000000000000000−2i2i
χ192222-2-222-2-2-2-22222-222-2-2-2-20000200000000000000002i2i−2i−2i00000000
χ202222-2-222-2-2-2-22222-222-2-2-2-2000020000000000000000−2i−2i2i2i00000000
χ212222-2-222-2-2-2-2-2-2-2-2-22222220000-20000000000000000000000002-200
χ222222-2-222-2-2-2-2-2-2-2-2-22222220000-2000000000000000000000000-2200
χ232222-2-2-2-222220000-22-200000000022-2-222−2−222−2−2000000002−22−20000
χ242222-2-2-2-222220000-22-200000000022-2-2−2−222−2−22200000000−22−220000
χ252222-2-2-2-222220000-22-2000000000-2-22222−2−222−2−200000000−22−220000
χ262222-2-2-2-222220000-22-2000000000-2-222−2−222−2−222000000002−22−20000
χ272222-2-2-2-2-222-200002-2200002i2i−2i−2i0000022−2−2−2−22200000000i2−i2−i2i20000
χ282222-2-2-2-2-222-200002-2200002i2i−2i−2i00000−2−22222−2−200000000−i2i2i2−i20000
χ292222-2-2-2-2-222-200002-220000−2i−2i2i2i0000022−2−2−2−22200000000−i2i2i2−i20000
χ302222-2-2-2-2-222-200002-220000−2i−2i2i2i00000−2−22222−2−200000000i2−i2−i2i20000
χ312-2-222-22-20-22022-2-20002-2000000000002-22-20000i2−i2i2−i2i2−i2i2−i200000000
χ322-2-222-22-20-22022-2-20002-2000000000002-22-20000−i2i2−i2i2−i2i2−i2i200000000
χ332-2-222-22-20-22022-2-20002-200000000000-22-220000i2−i2i2−i2−i2i2−i2i200000000
χ342-2-222-22-20-22022-2-20002-200000000000-22-220000−i2i2−i2i2i2−i2i2−i200000000
χ352-2-22-222-202-2022-2-2000-220000000000000002i−2i2i−2ii2−i2−i2i22−2−2200000000
χ362-2-22-222-202-2022-2-2000-220000000000000002i−2i2i−2i−i2i2i2−i2−222−200000000
χ372-2-22-222-202-2022-2-2000-22000000000000000−2i2i−2i2ii2−i2−i2i2−222−200000000
χ382-2-22-222-202-2022-2-2000-22000000000000000−2i2i−2i2i−i2i2i2−i22−2−2200000000
χ39444444-4-44-4-440000-4-440000000000000000000000000000000000000
χ40444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000
χ4144-4-40000400-422−2222−220000022−222-22-200022−22000000000000000000000000
χ4244-4-40000400-422−2222−220000022−22-22-22000−2222000000000000000000000000
χ4344-4-40000400-4−2222−222200000−22222-22-2000−2222000000000000000000000000
χ4444-4-40000400-4−2222−222200000−2222-22-2200022−22000000000000000000000000
χ4544-4-40000-400422−2222−2200000−22222i−2i−2i2i02i2−2i200000000000000000000000000
χ4644-4-40000-400422−2222−2200000−2222−2i2i2i−2i0−2i22i200000000000000000000000000
χ4744-4-40000-4004−2222−22220000022−222i−2i−2i2i0−2i22i200000000000000000000000000
χ4844-4-40000-4004−2222−22220000022−22−2i2i2i−2i02i2−2i200000000000000000000000000
χ494-4-444-44-40-440-4-444000-4400000000000000000000000000000000000
χ504-4-444-4-4404-400000000000000000000000002i2−2i2−2i22i20000000000000000
χ514-4-444-4-4404-40000000000000000000000000−2i22i22i2−2i20000000000000000
χ524-4-44-444-404-40-4-4440004-400000000000000000000000000000000000
χ534-4-44-44-440-4400000000000000000000022−22−222200000000000000000000
χ544-4-44-44-440-44000000000000000000000−222222−2200000000000000000000
χ558-88-80000000042−42−42420000000000000000000000000000000000000000
χ568-88-800000000−424242−420000000000000000000000000000000000000000

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