Finite Group Databasebeta

← Group #272372

Character table — Group #272372

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444444444244444444888888884444488888888888828
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1
χ31111111111111111111-1-111111-1-111111111-1-1-1111-1-1-1-1-1-1-111-1-1
χ41111111111111111111-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-111-1-111
χ511111111111111111-1-1111-111-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-11-1
χ611111111111111111-1-1111-111-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-11111-11
χ711111111111111111-1-1-1-11-111-111111111-1-1-1-1-11-1-1-1-111111-1-1-11
χ811111111111111111-1-1-1-11-111-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111-1
χ91111111111111-1-1111111-11-1-111111-1-1-1-1-1-11-1-1111-1-11-1-1-1-1-1-111
χ101111111111111-1-1111111-11-1-1111-1-11111-1-11-1-1-1-1-1111-1-11111-1-1
χ111111111111111-1-11111-1-1-11-1-11-1-111-1-1-1-1-1-1-11111111-11111-1-1-1-1
χ121111111111111-1-11111-1-1-11-1-11-1-1-1-11111-1-1-111-1-1-1-1-1-111-1-11111
χ131111111111111-1-111-1-111-1-1-1-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-11111111-1
χ141111111111111-1-111-1-111-1-1-1-1-1-1-1-1-11111111-1-1-11111-111-1-1-1-1-11
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-1111-1-1-1-111-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1111111-111-111-1-11-1-111-1-11-1
χ172222222-2-2-22-2222-2-2000020-2-20000000000000002i−2i00000002i−2i00
χ182222222-2-2-22-2222-2-2000020-2-2000000000000000−2i2i0000000−2i2i00
χ192222222-2-2-22-22-2-2-2-20000-20220000000000000002i−2i0000000−2i2i00
χ202222222-2-2-22-22-2-2-2-20000-2022000000000000000−2i2i00000002i−2i00
χ21222222-2222-22-200-2-222220-200-22200000000-20000000-200000000
χ22222222-2222-22-200-2-222-2-20-200-2-2-20000000020000000200000000
χ23222222-2222-22-200-2-2-2-22202002-2-200000000-20000000200000000
χ24222222-2222-22-200-2-2-2-2-2-202002220000000020000000-200000000
χ252222-2-222-2-222-2222-22-200-222-2-2000000002-200000000000000000
χ262222-2-222-2-222-2222-2-2200-2-22-2200000000-2200000000000000000
χ272222-2-222-2-222-2-2-22-22-20022-22-200000000-2200000000000000000
χ282222-2-222-2-222-2-2-22-2-22002-2-222000000002-200000000000000000
χ292222-2-22-2222-2-222-220000-20-220002222-2-200000-20000000000000
χ302222-2-22-2222-2-222-220000-20-22000-2-2-2-2220000020000000000000
χ312222-2-22-2222-2-2-2-2-220000202-200022-2-22200000-20000000000000
χ322222-2-22-2222-2-2-2-2-220000202-2000-2-222-2-20000020000000000000
χ332222-2-2-22-2-2-22200-222-2000-2002000000000002-20000002-2000000
χ342222-2-2-22-2-2-22200-222-2000-200200000000000-22000000-22000000
χ352222-2-2-22-2-2-22200-22-22000200-2000000000002-2000000-22000000
χ362222-2-2-22-2-2-22200-22-22000200-200000000000-220000002-2000000
χ37444444-4-4-4-4-4-4-40044000000000000000000000000000000000000
χ384444-4-4-4-444-4-44004-4000000000000000000000000000000000000
χ3944-4-44-4044-40-4000000000000004-40000000000000000000000000
χ4044-4-44-4044-40-400000000000000-440000000000000000000000000
χ4144-4-44-40-4-44040000000000000000000000000000002i2−2i2000000000
χ4244-4-44-40-4-4404000000000000000000000000000000−2i22i2000000000
χ4344-4-4-4404-440-400000004-400000000000000000000000000000000
χ4444-4-4-4404-440-40000000-4400000000000000000000000000000000
χ4544-4-4-440-44-404000000000000000000000000000000000002i2−2i20000
χ4644-4-4-440-44-40400000000000000000000000000000000000−2i22i20000
χ474-44-400-40004004-400000000000002i2−2i22i2−2i2000000000000000000000
χ484-44-400-40004004-40000000000000−2i22i2−2i22i2000000000000000000000
χ494-44-400-4000400-4400000000000002i2−2i2−2i22i2000000000000000000000
χ504-44-400-4000400-440000000000000−2i22i22i2−2i2000000000000000000000
χ518-88-8008000-8000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000000004-40000000000000000000
χ538-8-880000000000000000000000000000-440000000000000000000

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