Finite Group Databasebeta

← Group #250308

Character table — Group #250308

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222224448888888888888888881616161616161616161616161616161616161632
order12222244444444424444444448888888824444444444888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1
χ311111111111111111111-1-11-1-111-1-11111-1-1-1-1-11-1-1-1-1-1111-11111-1
χ411111111111111111111-1-11-1-111-1-1-1-1-1-111-1111-1-1-111-1-11-1-1-1-1-11
χ511111111111111111-1-1111111-1-1-1-1111111-111-111-1-1-1-1-1-1-1-1-111-1
χ611111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-11
χ711111111111111111-1-11-1-11-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-11-1-1111
χ811111111111111111-1-11-1-11-1-1-1-111-1-1-1-111111-1-1-11-1-111-1111-1-1-1
χ9111111111111111-1-111-111-111-1-1-1-11111111-1-11-1-11-1-111-1-1-1-1-1-11
χ10111111111111111-1-111-111-111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-11111-1
χ11111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-111111-11111-11-1-1-1-1-1
χ12111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-1111111
χ13111111111111111-1-1-1-1-111-1111111111111-1-1-1-1-1-1-111-1-11111-1-1-1
χ14111111111111111-1-1-1-1-111-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111
χ15111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111-1111-1-1-1-11-111-1-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-111111111-1-1-111-1
χ172222222-222-22-2-2-22222-200-2002200000000000-20000000-2000000
χ182222222-222-22-2-2-222-2-2-200-200-2-200000000000200000002000000
χ192222222-222-22-2-2-2-2-222200200-2-200000000000-200000002000000
χ202222222-222-22-2-2-2-2-2-2-2200200220000000000020000000-2000000
χ21222222-2-2-2-2-2-2-222000002-202-2000000000002-20000000000002-20
χ22222222-2-2-2-2-2-2-222000002-202-200000000000-22000000000000-220
χ23222222-2-2-2-2-2-2-22200000-220-22000000000002-2000000000000-220
χ24222222-2-2-2-2-2-2-22200000-220-2200000000000-220000000000002-20
χ252222-2-222-222-2-2-2200000220-2-2000022-2-22-2000000000000000000
χ262222-2-222-222-2-2-2200000220-2-20000-2-222-22000000000000000000
χ272222-2-222-222-2-2-2200000-2-2022000022-2-2-22000000000000000000
χ282222-2-222-222-2-2-2200000-2-20220000-2-2222-2000000000000000000
χ292222-2-2-222-222-22-22-200200-2000022000000200000-200000-200000
χ302222-2-2-222-222-22-22-200200-20000-2-2000000-200000200000200000
χ312222-2-2-222-222-22-2-2200-2002000022000000-200000200000-200000
χ322222-2-2-222-222-22-2-2200-20020000-2-2000000200000-200000200000
χ332222-2-2-2-22-2-222-222-200-22-22-22000000000000002-2000000000000
χ342222-2-2-2-22-2-222-222-200-2-2222-200000000000000-22000000000000
χ352222-2-2-2-22-2-222-22-220022-2-2-2200000000000000-22000000000000
χ362222-2-2-2-22-2-222-22-22002-22-22-2000000000000002-2000000000000
χ37444444-44-4-44-44-4-400000000000000000000000000000000000000
χ384444-4-44-4-44-4-444-400000000000000000000000000000000000000
χ3944-4-44-440-4-40400000000000000000000000000000000000022−22000
χ4044-4-44-440-4-404000000000000000000000000000000000000−2222000
χ4144-4-44-4-40440-4000004-40000000000000000000000000000000000
χ4244-4-44-4-40440-400000-440000000000000000000000000000000000
χ4344-4-4-44404-40-400000000000004-400000000000000000000000000
χ4444-4-4-44404-40-40000000000000-4400000000000000000000000000
χ4544-4-4-44-40-4404000000000000000000000000000000002i2−2i20000000
χ4644-4-4-44-40-440400000000000000000000000000000000−2i22i20000000
χ474-44-4000-4004000000000000000022−22002i2−2i20000000002i−2i000000000
χ484-44-4000-4004000000000000000022−2200−2i22i2000000000−2i2i000000000
χ494-44-4000-40040000000000000000−2222002i2−2i2000000000−2i2i000000000
χ504-44-4000-40040000000000000000−222200−2i22i20000000002i−2i000000000
χ518-88-8000800-8000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000004i−4i0000000000000000000000
χ538-8-880000000000000000000000000−4i4i0000000000000000000000

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