Finite Group Databasebeta

← Group #288706

Character table — Group #288706

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222222444448888888888816161616161616161616161616161616161616163232
order12222244444444488888888888882244444488888888888844
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-111-11111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111111111111111-1-1-1-1-11-1-11-1-1-1111-1-1-1-1-1-11-1-111
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1
χ51111111111111111111-1-11-1-11111-11-1-11-111-11111-1-1-1-1-111-1-1
χ61111111111111111111-1-11-1-11111-1-1-1-1-1-111-1-1-1-1-11111-1-1-111
χ71111111111111111111-1-11-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1
χ81111111111111111111-1-11-1-1-1-1-1-11-111-11-1-1-1-1-111-1-1-1-1-11111
χ9111111111111111-1-1-1-111-1-1-11111-111-111-1-1-1-1-11111-1-11-1-11-1
χ10111111111111111-1-1-1-111-1-1-11111-1-11-1-11-1-1-111-1-1-1-111111-11
χ11111111111111111-1-1-1-111-1-1-1-1-1-1-111-111-111-1-1-1-1-1-1-1111111-1
χ12111111111111111-1-1-1-111-1-1-1-1-1-1-11-1-11-1-111-1111111-1-11-1-1-11
χ13111111111111111-1-1-1-1-1-1-111111111-111-1-1-11-1-111-1-111-1-1-1-11
χ14111111111111111-1-1-1-1-1-1-11111111-1-11-1-1-1-1111-1-111-1-1-1111-1
χ15111111111111111-1-1-1-1-1-1-111-1-1-1-1-111-111111-1-1-1-111-1-1-111-11
χ16111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-11-1-111111111-1-111-1-1-11-1
χ1722222222-2-222-2-2-222-2-2222-2-2000000000000200000000-20000
χ1822222222-2-222-2-2-222-2-2-2-2222000000000000-20000000020000
χ1922222222-2-222-2-2-2-2-22222-222000000000000-200000000-20000
χ2022222222-2-222-2-2-2-2-222-2-2-2-2-200000000000020000000020000
χ21222222-2-2-2-2-2-2-2220000000002i2i−2i−2i0000000002i−2i00000002-200
χ22222222-2-2-2-2-2-2-2220000000002i2i−2i−2i000000000−2i2i0000000-2200
χ23222222-2-2-2-2-2-2-222000000000−2i−2i2i2i0000000002i−2i0000000-2200
χ24222222-2-2-2-2-2-2-222000000000−2i−2i2i2i000000000−2i2i00000002-200
χ252222-2-22-2222-2-2-22222-200-200000020-2-2020000000000000000
χ262222-2-22-2222-2-2-22222-200-2000000-20220-20000000000000000
χ272222-2-22-2222-2-2-22-2-2-22002000000202-20-20000000000000000
χ282222-2-22-2222-2-2-22-2-2-22002000000-20-22020000000000000000
χ292222-2-22-2-2-22-222-222-2200-2002i−2i2i−2i0000002i−2i00000000000000
χ302222-2-22-2-2-22-222-222-2200-200−2i2i−2i2i000000−2i2i00000000000000
χ312222-2-22-2-2-22-222-2-2-22-2002002i−2i2i−2i000000−2i2i00000000000000
χ322222-2-22-2-2-22-222-2-2-22-200200−2i2i−2i2i0000002i−2i00000000000000
χ332222-2-2-2222-22-22-20000000002-2-220200-20000002-2000000000
χ342222-2-2-2222-22-22-20000000002-2-220-2002000000-22000000000
χ352222-2-2-2222-22-22-2000000000-222-20200-2000000-22000000000
χ362222-2-2-2222-22-22-2000000000-222-20-20020000002-2000000000
χ37444444-4-444-4-44-4-400000000000000000000000000000000000
χ384444-4-4-44-4-4-444-4400000000000000000000000000000000000
χ394-44-44-44400-4-4000000000000000000000000000000022−2200000
χ404-44-44-44400-4-40000000000000000000000000000000−222200000
χ414-44-44-4-4-4004400000004i−4i00000000000000000000000000000
χ424-44-44-4-4-400440000000−4i4i00000000000000000000000000000
χ434-44-4-444-400-44000000000000000000000000000002i2−2i20000000
χ444-44-4-444-400-4400000000000000000000000000000−2i22i20000000
χ454-44-4-44-44004-400000000004i−4i00000000000000000000000000
χ464-44-4-44-44004-40000000000−4i4i00000000000000000000000000
χ4788-8-800008-80000000000000000000000000000000000000000
χ4888-8-80000-880000000000000000000000000000000000000000
χ498-8-880000000000042−42000000000000000000000000000000000
χ508-8-8800000000000−4242000000000000000000000000000000000

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