Finite Group Databasebeta

← Group #272396

Character table — Group #272396

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444444444222444444888888884444488888888888848
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1
χ31111111111111111111-1-111-11-111-1-11111-1111-1111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111-1-111-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111-11
χ511111111111111111-1-1111111111-1-111111-1-1-111-1-111-1-1-1-1-111-1-1
χ611111111111111111-1-11111111-1-1-1-1-1-1-1-11-1-1-11-111-1-1-1-1-111-1-111
χ711111111111111111-1-1-1-111-11-111111111-1-1-1-1-11-1-1-1-111111-1-1-11
χ811111111111111111-1-1-1-111-11-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1111-1
χ91111111111111-1-1111111-1-11-111111-1-1-1-1-11-1-1-11-1-1111-1-1-1-1-1-111
χ101111111111111-1-1111111-1-11-11-1-1111111-11-1-1-1-111-1-11-1-11111-1-1
χ111111111111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-11111111-1
χ121111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-111-1-1-1-1-11
χ131111111111111-1-111-1-111-1-11-1111-1-1-1-1-1-1-1-111-111111-11111-1-1-1-1
χ141111111111111-1-111-1-111-1-11-11-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-11111
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11-1111111-1-11-1-1-1-111-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111111-1111-1-1-1111-1-111-1-11-1
χ172222222-2-22-2-2222-2-20000-2-202000000000000000002i−2i000002i−2i00
χ182222222-2-22-2-2222-2-20000-2-20200000000000000000−2i2i00000−2i2i00
χ192222222-2-22-2-22-2-2-2-20000220-2000000000000000002i−2i00000−2i2i00
χ202222222-2-22-2-22-2-2-2-20000220-200000000000000000−2i2i000002i−2i00
χ21222222-222-222-200-2-2222200-20-2002200000-200000000-200000000
χ22222222-222-222-200-2-222-2-20020200-2-200000-200000000200000000
χ23222222-222-222-200-2-2-2-22200-20-200-2-200000200000000200000000
χ24222222-222-222-200-2-2-2-2-2-200202002200000200000000-200000000
χ252222-2-22222-2-2-222-2200002-20-20220022-2-200000-20000000000000
χ262222-2-22222-2-2-222-2200002-20-20-2-200-2-2220000020000000000000
χ272222-2-22222-2-2-2-2-2-220000-220202200-2-22200000-20000000000000
χ282222-2-22222-2-2-2-2-2-220000-22020-2-20022-2-20000020000000000000
χ292222-2-22-2-2222-2222-2002-2-22-2-2200000000-2000200000000000000
χ302222-2-22-2-2222-2222-200-22-222-2-2000000002000-200000000000000
χ312222-2-22-2-2222-2-2-22-2002-22-2-222000000002000-200000000000000
χ322222-2-22-2-2222-2-2-22-200-222-222-200000000-2000200000000000000
χ332222-2-2-2-2-2-222200-22002-20020-200000000002-200000002-2000000
χ342222-2-2-2-2-2-222200-22002-20020-20000000000-220000000-22000000
χ352222-2-2-2-2-2-222200-2200-2200-20200000000002-20000000-22000000
χ362222-2-2-2-2-2-222200-2200-2200-2020000000000-2200000002-2000000
χ37444444-4-4-4-4-4-4-40044000000000000000000000000000000000000
χ384444-4-4-444-4-4-44004-4000000000000000000000000000000000000
χ3944-4-44-404-404-40000000000000000000000000000000000022−220000
χ4044-4-44-404-404-400000000000000000000000000000000000−22220000
χ4144-4-44-40-440-44000004-40000000000000000000000000000000000
χ4244-4-44-40-440-4400000-440000000000000000000000000000000000
χ4344-4-4-4404-40-4400000000000000004-400000000000000000000000
χ4444-4-4-4404-40-440000000000000000-4400000000000000000000000
χ4544-4-4-440-4404-4000000000000000000000000000022−2200000000000
χ4644-4-4-440-4404-40000000000000000000000000000−222200000000000
χ474-4-4400400-40004-4000000000002i2−2i2002i2−2i2000000000000000000000
χ484-4-4400400-40004-400000000000−2i22i200−2i22i2000000000000000000000
χ494-4-4400400-4000-44000000000002i2−2i200−2i22i2000000000000000000000
χ504-4-4400400-4000-4400000000000−2i22i2002i2−2i2000000000000000000000
χ518-88-800000000000000000000000000004i−4i0000000000000000000
χ528-88-80000000000000000000000000000−4i4i0000000000000000000
χ538-8-8800-80080000000000000000000000000000000000000000000

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