Finite Group Databasebeta

← Group #251156

Character table — Group #251156

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444244444444888888444444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11-11-1111-1-1-1-1-1111-1-1-1-1-1-1
χ311111111111111111111111-1-11-1-111111-11-1-1-1-1-1-111-1-1-1-1-1-1-1111
χ411111111111111111111111-1-11-1-1-1-1-1-11111-1-1-111-1-11-1-1-1111-1-1-1
χ511111111111111111-11-111-111-1-1-11111-1-1-1-11111111-1-1-1-111-1-1-1-1
χ611111111111111111-11-111-111-1-1-1-1-1-1-1-11-11111-1-1-1-11-1-1-1-1-11111
χ711111111111111111-11-111-1-1-1-1111111-11-11-1-1-1-1-1111111-1-11-1-1-1
χ811111111111111111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1111
χ9111111111111-1-11111-11-1-11111111111-1-1-1-11-1-1-1-1-1-111-1-111111-1
χ10111111111111-1-11111-11-1-1111111-1-1-1-1-11-111-1-11111-11-1-1-1-1-1-1-11
χ11111111111111-1-11111-11-1-11-1-11-1-11111-11-11-11111-1-1-1-111-1-1-111-1
χ12111111111111-1-11111-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1111-111111-1-11
χ13111111111111-1-1111-1-1-1-1-1-111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-11
χ14111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-11-11-11-1-111111-111-1-1111-1
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-11111111-11-1-11111-1-111-1-1-1-11-1-11
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-111-11-1-111-111-1
χ172222222-222-2200-2-2-220-200-22222200000000-20000000-200000000
χ182222222-222-2200-2-2-220-200-2-2-22-2-20000000020000000200000000
χ192222222-222-2200-2-2-2-20200222-2-2-200000000-20000000200000000
χ202222222-222-2200-2-2-2-202002-2-2-2220000000020000000-200000000
χ21222222-22-2-22-222-22-2020-2-2000000000000000002-20000002-20000
χ22222222-22-2-22-222-22-2020-2-200000000000000000-22000000-220000
χ23222222-22-2-22-2-2-2-22-20-2022000000000000000002-2000000-220000
χ24222222-22-2-22-2-2-2-22-20-202200000000000000000-220000002-20000
χ252222-2-222-222-222-2-220-202-20000000000020-20000000200000-2000
χ262222-2-222-222-222-2-220-202-200000000000-2020000000-2000002000
χ272222-2-222-222-2-2-2-2-22020-220000000000020-20000000-2000002000
χ282222-2-222-222-2-2-2-2-22020-2200000000000-2020000000200000-2000
χ292222-2-2-222-222222-2-22-22-22-200-200000020-2000000000000000000
χ302222-2-2-222-222222-2-2-2-2-2-222002000000-202000000000000000000
χ312222-2-2-222-222-2-22-2-22222-2-200-2000000-202000000000000000000
χ322222-2-2-222-222-2-22-2-2-22-22-2200200000020-2000000000000000000
χ332222-2-2-2-22-2-2200-22220-200200-2000000000002-20000002-2000000
χ342222-2-2-2-22-2-2200-22220-200200-200000000000-22000000-22000000
χ352222-2-2-2-22-2-2200-222-20200-2002000000000002-2000000-22000000
χ362222-2-2-2-22-2-2200-222-20200-200200000000000-220000002-2000000
χ37444444-4-4-4-4-4-4004-44000000000000000000000000000000000000
χ384444-4-44-4-44-4-40044-4000000000000000000000000000000000000
χ3944-4-4000400-404-40000000000000022-2-20000000002-20000000000
χ4044-4-4000400-404-400000000000000-2-222000000000-220000000000
χ4144-4-4000400-40-440000000000000022-2-2000000000-220000000000
χ4244-4-4000400-40-4400000000000000-2-2220000000002-20000000000
χ434-4-444-4404-40-4000000000000000022−2222−22000000000000000000000
χ444-4-444-4404-40-40000000000000000−2222−2222000000000000000000000
χ454-4-444-4-40-4404000000000004i−4i0000000000000000000000000000
χ464-4-444-4-40-440400000000000−4i4i0000000000000000000000000000
χ474-4-44-4440-4-404000000000000004i−4i0000000000000000000000000
χ484-4-44-4440-4-40400000000000000−4i4i0000000000000000000000000
χ494-4-44-44-40440-4000000000000000000000000000000000000002i2−2i20
χ504-4-44-44-40440-400000000000000000000000000000000000000−2i22i20
χ5188-8-8000-8008000000000000000000000000000000000000000000
χ528-88-800000000000000000000000022−22−2222000000000000000000000
χ538-88-8000000000000000000000000−222222−22000000000000000000000

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