Finite Group Databasebeta

← Group #274002

Character table — Group #274002

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244488888888888888888888161616161616161616161616161616163232
order12222244444444424444444448888888888244448888888888848
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1
χ31111111111111111111-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1111-1-1-1-1
χ41111111111111111111-1-11111-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-111
χ611111111111111111-1-1111-1-11-1-111-1-11111-1-1-11-11-1-1-11-111111-1-1
χ711111111111111111-1-1-1-11-1-1111-1-11111111-1-1-11-1111-11-1-1-111-1-1
χ811111111111111111-1-1-1-11-1-11-1-1-1-111-1-1-1-11-1-1-111-1-1-1-11111-1-111
χ9111111111111111-1-11111-111-111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-1-1111-1
χ10111111111111111-1-11111-111-1-1-1-1-1-1-111111-1-111-1-111-1-1-111-1-1-11
χ11111111111111111-1-111-1-1-111-11111111111-1-1-1-1-111-1-1111-1-1-1-1-11
χ12111111111111111-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-111111-1
χ13111111111111111-1-1-1-111-1-1-1-111-1-1111111-1111-1-11-1-1-11-111-1-11-1
χ14111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1111-11-111-111-1-111-11
χ15111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-11-11-1-11-1-11111-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-111-1111-11-1-1-1-11-1
χ17222222-222-222-2-2-22-20022-20020022000000000-200000-200000000
χ18222222-222-222-2-2-22-200-2-2-200200-2-2000000000200000200000000
χ19222222-222-222-2-2-2-220022200-200-2-2000000000-200000200000000
χ20222222-222-222-2-2-2-2200-2-2200-20022000000000200000-200000000
χ21222222-2-2-2-2-2-222-2002-20002-20000000000000000002i−2i0002i−2i0000
χ22222222-2-2-2-2-2-222-2002-20002-2000000000000000000−2i2i000−2i2i0000
χ23222222-2-2-2-2-2-222-200-22000-220000000000000000002i−2i000−2i2i0000
χ24222222-2-2-2-2-2-222-200-22000-22000000000000000000−2i2i0002i−2i0000
χ252222-2-22222-2-2-22-20022000-2-202200000000000002-20000-2000000
χ262222-2-22222-2-2-22-20022000-2-20-2-20000000000000-2200002000000
χ272222-2-22222-2-2-22-200-2-2000220220000000000000-2-200002000000
χ282222-2-22222-2-2-22-200-2-2000220-2-20000000000000220000-2000000
χ292222-2-22-2-22222-2-22-20000200-20000220000-2000200000-20000000
χ302222-2-22-2-22222-2-22-20000200-20000-2-200002000-20000020000000
χ312222-2-22-2-22222-2-2-220000-200200002200002000-200000-20000000
χ322222-2-22-2-22222-2-2-220000-20020000-2-20000-200020000020000000
χ332222-2-2-2-2-2-222-222222-200-2-22-2000000000002-2000000000000000
χ342222-2-2-2-2-2-222-22222-2200-22-2-200000000000-22000000000000000
χ352222-2-2-2-2-2-222-222-2-22-2002-22200000000000-22000000000000000
χ362222-2-2-2-2-2-222-222-2-2-220022-22000000000002-2000000000000000
χ374444444-4-44-4-4-4-4400000000000000000000000000000000000000
χ384444-4-4-444-4-4-44-4400000000000000000000000000000000000000
χ394-44-400-400400000000000000022−22002i2−2i22i2i−2i−2i000000000000000000
χ404-44-400-400400000000000000022−2200−2i22i2−2i−2i2i2i000000000000000000
χ414-44-400-4004000000000000000−2222002i2−2i2−2i−2i2i2i000000000000000000
χ424-44-400-4004000000000000000−222200−2i22i22i2i−2i−2i000000000000000000
χ434-4-444-404-404-400000000000000000002i2−2i22i2−2i2000000000000000000
χ444-4-444-404-404-40000000000000000000−2i22i2−2i22i2000000000000000000
χ454-4-444-40-440-4400000004i−4i00000000000000000000000000000000
χ464-4-444-40-440-440000000−4i4i00000000000000000000000000000000
χ474-4-44-4404-40-440000000000000004i−4i000000000000000000000000
χ484-4-44-4404-40-44000000000000000−4i4i000000000000000000000000
χ494-4-44-440-4404-400000000000000000000000000000000000002i2−2i200
χ504-4-44-440-4404-40000000000000000000000000000000000000−2i22i200
χ5188-8-800000000000000000000000000022−22−2222000000000000000000
χ5288-8-8000000000000000000000000000−222222−22000000000000000000
χ538-88-800800-80000000000000000000000000000000000000000000

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