Finite Group Databasebeta

← Group #317290

Character table — Group #317290

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444444444488888881616161616161616161616161616161632323232
order12224444244448888888888888888822444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1111-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-11-1-1-1111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111-1-1-1-11-1-1-1-1-1-11-1111-111-1-1-1-1-1-111-1-111
χ71111111111111111111-1-1-1-11-1-1-1-1-1-1-11-1-1-11-1-1111111-1-1-1-111
χ81111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ91111111111111-1-1-1-1-1-11111-111-1-1-1-1111-1-11-1-111-1-1-1-1111-11-1
χ101111111111111-1-1-1-1-1-11111-111-1-1-1-11-11-1-1-11111-1-111-1-1-11-11
χ111111111111111-1-1-1-1-1-11111-111-1-1-1-1-11-1111-1-1-1-111-1-111-11-11
χ121111111111111-1-1-1-1-1-11111-111-1-1-1-1-1-1-111-111-1-11111-1-11-11-1
χ131111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111-1-111-1-1-1-11-1-11
χ141111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1-1-1-1-1111111-111-1
χ151111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11111111-1-1-1-1-1-1-111-1
χ161111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-111111-1-11
χ1722222222-2-22-2-22222-2-22222-2-2-222-2-200000000000000000000
χ1822222222-2-22-2-22222-2-2-2-2-2-2-222-2-22200000000000000000000
χ1922222222-2-22-2-2-2-2-2-22222222-2-2-2-22200000000000000000000
χ2022222222-2-22-2-2-2-2-2-222-2-2-2-222222-2-200000000000000000000
χ21222222-2-222-2-2-222-2-2220000-2000000000000002i−2i2i−2i00000000
χ22222222-2-222-2-2-222-2-2220000-200000000000000−2i2i−2i2i00000000
χ23222222-2-222-2-2-2-2-222-2-200002000000000000002i−2i−2i2i00000000
χ24222222-2-222-2-2-2-2-222-2-20000200000000000000−2i2i2i−2i00000000
χ25222222-2-2-2-2-22222-2-2-2-20000200000020-22-2000000000000000
χ26222222-2-2-2-2-22222-2-2-2-200002000000-202-22000000000000000
χ27222222-2-2-2-2-222-2-222220000-200000020-2-22000000000000000
χ28222222-2-2-2-2-222-2-222220000-2000000-2022-2000000000000000
χ292222-2-2-2-22-222-20000002i2i−2i−2i02i−2i00000000002-200002i−2i000000
χ302222-2-2-2-22-222-20000002i2i−2i−2i02i−2i0000000000-220000−2i2i000000
χ312222-2-2-2-22-222-2000000−2i−2i2i2i0−2i2i00000000002-20000−2i2i000000
χ322222-2-2-2-22-222-2000000−2i−2i2i2i0−2i2i0000000000-2200002i−2i000000
χ332222-2-2-2-2-222-220000002i2i−2i−2i0−2i2i000002000-2000000002i−2i0000
χ342222-2-2-2-2-222-220000002i2i−2i−2i0−2i2i00000-2000200000000−2i2i0000
χ352222-2-2-2-2-222-22000000−2i−2i2i2i02i−2i000002000-200000000−2i2i0000
χ362222-2-2-2-2-222-22000000−2i−2i2i2i02i−2i00000-20002000000002i−2i0000
χ374444-4-4444-4-4-440000000000000000000000000000000000000
χ384444-4-444-44-44-40000000000000000000000000000000000000
χ3944-4-44-4000000000004-42i2−2i22i2−2i2000002i2−2i200000000000000000000
χ4044-4-44-4000000000004-4−2i22i2−2i22i200000−2i22i200000000000000000000
χ4144-4-44-400000000000-442i2−2i22i2−2i200000−2i22i200000000000000000000
χ4244-4-44-400000000000-44−2i22i2−2i22i2000002i2−2i200000000000000000000
χ4344-4-4-4400000004i−4i000022−22−22220002i2−2i20000000000000000000000
χ4444-4-4-4400000004i−4i0000−222222−22000−2i22i20000000000000000000000
χ4544-4-4-440000000−4i4i000022−22−2222000−2i22i20000000000000000000000
χ4644-4-4-440000000−4i4i0000−222222−220002i2−2i20000000000000000000000
χ478-88-8000000000004i2−4i2000000000000000000000000000000000
χ488-88-800000000000−4i24i2000000000000000000000000000000000
χ498-8-88008i−8i000000000000000000000000000000000000000000
χ508-8-8800−8i8i000000000000000000000000000000000000000000

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