Finite Group Databasebeta

← Group #250306

Character table — Group #250306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222224448888888888888888881616161616161616161616161616161616161632
order12222244444444424444444448888888822444444444888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-11-111-1-1-111-1-1-1-111-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111-11-1-111111-1-1-1-1-1-1-1-111-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11
χ5111111111111111111-1-11-1-11111-1-11111-1-11-1-1-1-1-1-1-1-1111-11111-1
χ6111111111111111111-1-11-1-11111-1-1-1-1-1-1-111-1111-1-111-1-11-1-1-1-1-11
χ7111111111111111111-1-11-1-1-1-1-1-11111111-1-11-1-1-1-1-111-1-1-11-1-1111
χ8111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111-1111-1-1-1
χ9111111111111111-1-1-111-11111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-11
χ10111111111111111-1-1-111-11111-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1-11111-1
χ11111111111111111-1-1-111-111-1-111111111-11-1-11-1-1-1-111-1-11111-1-1-1
χ12111111111111111-1-1-111-111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111
χ13111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-11-1-111111111-11-1-1-1-1-1
χ14111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-11-1-111-1-1-1-1-1111111
χ15111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-11-11111-1-1-1-11-111-1-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-1-11111111-1-1-111-1
χ172222222-222-22-2-2-222-200-200222200000000-20000000000-2000000
χ182222222-222-22-2-2-222-200-200-2-2-2-200000000200000000002000000
χ192222222-222-22-2-2-2-2-220020022-2-200000000-200000000002000000
χ202222222-222-22-2-2-2-2-2200200-2-2220000000020000000000-2000000
χ21222222-2-2-2-2-2-2-2220002-202-20000000000000002-200000000002-20
χ22222222-2-2-2-2-2-2-2220002-202-2000000000000000-220000000000-220
χ23222222-2-2-2-2-2-2-222000-220-220000000000000002-20000000000-220
χ24222222-2-2-2-2-2-2-222000-220-22000000000000000-2200000000002-20
χ252222-2-222-222-2-2-22000220-2-200000022-2-20200-2000000000000000
χ262222-2-222-222-2-2-22000220-2-2000000-2-2220-2002000000000000000
χ272222-2-222-222-2-2-22000-2-202200000022-2-20-2002000000000000000
χ282222-2-222-222-2-2-22000-2-2022000000-2-2220200-2000000000000000
χ292222-2-2-222-222-22-22-2200-2000000220000200-20000000000-200000
χ302222-2-2-222-222-22-22-2200-2000000-2-20000-20020000000000200000
χ312222-2-2-222-222-22-2-22-2002000000220000-20020000000000-200000
χ322222-2-2-222-222-22-2-22-2002000000-2-20000200-20000000000200000
χ332222-2-2-2-22-2-222-222-2-22-22-22000000000000000002-200000000000
χ342222-2-2-2-22-2-222-222-2-2-2222-200000000000000000-2200000000000
χ352222-2-2-2-22-2-222-22-2222-2-2-2200000000000000000-2200000000000
χ362222-2-2-2-22-2-222-22-222-22-22-2000000000000000002-200000000000
χ37444444-44-4-44-44-4-400000000000000000000000000000000000000
χ384444-4-44-4-44-4-444-400000000000000000000000000000000000000
χ3944-4-4000-4004000000000000000022−22002i2−2i20000000002i−2i000000000
χ4044-4-4000-4004000000000000000022−2200−2i22i2000000000−2i2i000000000
χ4144-4-4000-40040000000000000000−2222002i2−2i2000000000−2i2i000000000
χ4244-4-4000-40040000000000000000−222200−2i22i20000000002i−2i000000000
χ434-44-44-4404-40-40000000000000000000000000000000022−220000000
χ444-44-44-4404-40-400000000000000000000000000000000−22220000000
χ454-44-44-4-40-440400000000000004i−4i00000000000000000000000000
χ464-44-44-4-40-44040000000000000−4i4i00000000000000000000000000
χ474-44-4-4440-4-404000000000004i−4i0000000000000000000000000000
χ484-44-4-4440-4-40400000000000−4i4i0000000000000000000000000000
χ494-44-4-44-40440-40000000000000000000000000000000000002i2−2i2000
χ504-44-4-44-40440-4000000000000000000000000000000000000−2i22i2000
χ5188-8-8000800-8000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000004i−4i0000000000000000000000
χ538-8-880000000000000000000000000−4i4i0000000000000000000000

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