Finite Group Databasebeta

← Group #253872

Character table — Group #253872

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222244224444424444444422444444444444444888888
χ111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1111-11-111-11-1-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111-1-1-1-11-1-1-1-1-1-11-11-1-1-111111111-1-1
χ5111111111111111111-1-11111-111-11-11-11-11-1-1-1-1-1-11111-1-1
χ6111111111111111111-1-11111-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1
χ8111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-1-1-1111111
χ91111111111-1-1111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ101111111111-1-1111-1-1-11111111-1-1-11-11-1-1-1-111-1-111-1-111-11
χ111111111111-1-1111-1-1-111-1-1-1-11111-11-1-11-11-1-1-1-111-1-1111-1
χ121111111111-1-1111-1-1-111-1-1-1-11-1-11111-11-11-1-111-1-111-1-1-11
χ131111111111-1-1111-1-1-1-1-11111-1111-11-11-11-1-1-1-1-11111-1-1-11
χ141111111111-1-1111-1-1-1-1-11111-1-1-111111-11-1-1-111-1-1-1-1111-1
χ151111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-11
χ161111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-11111-1-11-1
χ1722222222-2-2222-2-2-22-20022-2-200000000-202000000000000
χ1822222222-2-2222-2-2-22-200-2-2220000000020-2000000000000
χ1922222222-2-2-2-22-2-22-220022-2-20000000020-2000000000000
χ2022222222-2-2-2-22-2-22-2200-2-22200000000-202000000000000
χ21222222-2-22222-2-2-2-2-2200000000020-2000002-20000000000
χ22222222-2-22222-2-2-2-2-22000000000-20200000-220000000000
χ23222222-2-222-2-2-2-2-222-200000000020-200000-220000000000
χ24222222-2-222-2-2-2-2-222-2000000000-202000002-20000000000
χ25222222-2-2-2-222-2222-2-2220000-2000000-2020000000000000
χ26222222-2-2-2-222-2222-2-2-2-20000200000020-20000000000000
χ27222222-2-2-2-2-2-2-222-222220000-200000020-20000000000000
χ28222222-2-2-2-2-2-2-222-222-2-200002000000-2020000000000000
χ292222-2-2-2-22-20022-2000002i−2i2i−2i000020-20000000000002i−2i00
χ302222-2-2-2-22-20022-2000002i−2i2i−2i0000-202000000000000−2i2i00
χ312222-2-2-2-22-20022-200000−2i2i−2i2i000020-2000000000000−2i2i00
χ322222-2-2-2-22-20022-200000−2i2i−2i2i0000-2020000000000002i−2i00
χ332222-2-2-2-2-22002-22000002i−2i−2i2i02-2000000000000002i−2i0000
χ342222-2-2-2-2-22002-22000002i−2i−2i2i0-2200000000000000−2i2i0000
χ352222-2-2-2-2-22002-2200000−2i2i2i−2i02-200000000000000−2i2i0000
χ362222-2-2-2-2-22002-2200000−2i2i2i−2i0-22000000000000002i−2i0000
χ374444-4-4444-400-4-4400000000000000000000000000000000
χ384444-4-444-4400-44-400000000000000000000000000000000
χ3944-4-4-4400004i−4i00000000000000000000000002-22i−2i000000
χ4044-4-4-4400004i−4i0000000000000000000000000-22−2i2i000000
χ4144-4-4-440000−4i4i00000000000000000000000002-2−2i2i000000
χ4244-4-4-440000−4i4i0000000000000000000000000-222i−2i000000
χ4388-8-88-800000000000000000000000000000000000000000
χ448-88-8008i−8i000000000000000000000000000000000000000
χ458-88-800−8i8i000000000000000000000000000000000000000
χ468-8-88000000000000004-4000000000000000000000000000
χ478-8-8800000000000000-44000000000000000000000000000

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