Finite Group Databasebeta

← Group #288709

Character table — Group #288709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222222444448888888888816161616161616161616161616161616161616163232
order12222244444444488888888888882444444488888888888844
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-11-1111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-11-11-1-1111-1-1-1-1-1-11-1-111
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1
χ5111111111111111111-1-111-1-11111-1-1-11-1111-11111-1-1-1-1-111-1-1
χ6111111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-11111-1-1-111
χ7111111111111111111-1-111-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1
χ8111111111111111111-1-111-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-1-1-1-11111
χ9111111111111111-1-1-111-1-1-1-11111-1-11111-1-1-1-1-11111-1-11-1-11-1
χ10111111111111111-1-1-111-1-1-1-11111-1-11-11-1-1-1-111-1-1-1-111111-11
χ11111111111111111-1-1-111-1-1-1-1-1-1-1-111-11-1111-1-1-1-1-1-1-1111111-1
χ12111111111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1111111-1-11-1-1-11
χ13111111111111111-1-1-1-1-1-1-111111111-11-11-1-11-1-111-1-111-1-1-1-11
χ14111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-1-1111-1
χ15111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-111-11
χ16111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-11-11-11111111-1-111-1-1-11-1
χ17222222222-2-22-2-2-222222-2-2-2-2000000000000200000000-20000
χ18222222222-2-22-2-2-2222-2-2-2-222000000000000-20000000020000
χ19222222222-2-22-2-2-2-2-2-2222222000000000000-200000000-20000
χ20222222222-2-22-2-2-2-2-2-2-2-222-2-200000000000020000000020000
χ21222222-2-2-2-2-2-22-220000000002i2i−2i−2i0000000002i−2i00000002-200
χ22222222-2-2-2-2-2-22-220000000002i2i−2i−2i000000000−2i2i0000000-2200
χ23222222-2-2-2-2-2-22-22000000000−2i−2i2i2i0000000002i−2i0000000-2200
χ24222222-2-2-2-2-2-22-22000000000−2i−2i2i2i000000000−2i2i00000002-200
χ252222-2-22-2222-2-2-2222-2002-20000002-220-200000000000000000
χ262222-2-22-2222-2-2-2222-2002-2000000-22-20200000000000000000
χ272222-2-22-2222-2-2-22-2-2200-220000002-2-20200000000000000000
χ282222-2-22-2222-2-2-22-2-2200-22000000-2220-200000000000000000
χ292222-2-22-22-2-2-222-222-200-22002i−2i2i−2i0000002i−2i00000000000000
χ302222-2-22-22-2-2-222-222-200-2200−2i2i−2i2i000000−2i2i00000000000000
χ312222-2-22-22-2-2-222-2-2-22002-2002i−2i2i−2i000000−2i2i00000000000000
χ322222-2-22-22-2-2-222-2-2-22002-200−2i2i−2i2i0000002i−2i00000000000000
χ332222-2-2-22-22222-2-20000000002-2-2200020-2000002-2000000000
χ342222-2-2-22-22222-2-20000000002-2-22000-20200000-22000000000
χ352222-2-2-22-22222-2-2000000000-222-200020-200000-22000000000
χ362222-2-2-22-22222-2-2000000000-222-2000-202000002-2000000000
χ37444444-4-4-444-4-44-400000000000000000000000000000000000
χ384444-4-4-44-4-4-44-44400000000000000000000000000000000000
χ3944-4-44-44-4-400400000000004-400000000000000000000000000
χ4044-4-44-44-4-40040000000000-4400000000000000000000000000
χ4144-4-44-4-44400-40000000000000000000000000000022−220000000
χ4244-4-44-4-44400-400000000000000000000000000000−22220000000
χ4344-4-4-4444-400-40000004-4000000000000000000000000000000
χ4444-4-4-4444-400-4000000-44000000000000000000000000000000
χ4544-4-4-44-4-4400400000000000000000000000000000002i2−2i200000
χ4644-4-4-44-4-440040000000000000000000000000000000−2i22i200000
χ478-88-80000000000042−42000000000000000000000000000000000
χ488-88-800000000000−4242000000000000000000000000000000000
χ498-8-88000008-8000000000000000000000000000000000000000
χ508-8-8800000-88000000000000000000000000000000000000000

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