Finite Group Databasebeta

← Group #289133

Character table — Group #289133

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222224444444448888888881616161616161616161616161616161632323232
order12222244444444488888888888888824444444888888882488
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-111-111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ9111111111111111-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-111-1-111-1-11-11-1
χ10111111111111111-1-1-1-1-1-1-11111-1-1-1-11-111-11-1-111-1-1-1-111-11-11
χ11111111111111111-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-111-1-11111-1-1-11-11
χ12111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1-111-1-1111-11-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-1-1-111-111-1
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-111111-111-1111-1-1-1-111-1-11-1-11
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-1-1-11111-1-1111-1-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11-1-1111111-1-1-111-1
χ1722222222-2-222-2-2-222-2-2-2-220000000002-20-2200000000000000
χ1822222222-2-222-2-2-222-2-2-2-22000000000-2202-200000000000000
χ1922222222-2-222-2-2-2-2-22222-2000000000220-2-200000000000000
χ2022222222-2-222-2-2-2-2-22222-2000000000-2-202200000000000000
χ21222222-2-2-2-2-2-2-22200000002i2i−2i−2i00000000002-2002i−2i00000000
χ22222222-2-2-2-2-2-2-22200000002i2i−2i−2i0000000000-2200−2i2i00000000
χ23222222-2-2-2-2-2-2-2220000000−2i−2i2i2i00000000002-200−2i2i00000000
χ24222222-2-2-2-2-2-2-2220000000−2i−2i2i2i0000000000-22002i−2i00000000
χ252222-2-22-2222-2-2-222222-2-2-2000000000000000000002-22-20000
χ262222-2-22-2222-2-2-222222-2-2-200000000000000000000-22-220000
χ272222-2-22-2222-2-2-22-2-2-2-2222000000000000000000002-2-220000
χ282222-2-22-2222-2-2-22-2-2-2-222200000000000000000000-222-20000
χ292222-2-22-2-2-22-222-222-2-222-22i−2i2i−2i2i2i−2i−2i00000000000000000000
χ302222-2-22-2-2-22-222-222-2-222-2−2i2i−2i2i−2i−2i2i2i00000000000000000000
χ312222-2-22-2-2-22-222-2-2-222-2-222i−2i2i−2i−2i−2i2i2i00000000000000000000
χ322222-2-22-2-2-22-222-2-2-222-2-22−2i2i−2i2i2i2i−2i−2i00000000000000000000
χ332222-2-2-2222-22-22-200000002-2-220000200-200002-20000000000
χ342222-2-2-2222-22-22-200000002-2-220000-20020000-220000000000
χ352222-2-2-2222-22-22-20000000-222-20000200-20000-220000000000
χ362222-2-2-2222-22-22-20000000-222-20000-200200002-20000000000
χ37444444-4-444-4-44-4-400000000000000000000000000000000000
χ384444-4-4-44-4-4-444-4400000000000000000000000000000000000
χ394-4-444-44400-4-4000000000000002i2−2i22i2−2i200000000000000000000
χ404-4-444-44400-4-400000000000000−2i22i2−2i22i200000000000000000000
χ414-4-444-4-4-40044000004-44-400000000000000000000000000000
χ424-4-444-4-4-4004400000-44-4400000000000000000000000000000
χ434-4-44-444-400-440000000000000022−22−222200000000000000000000
χ444-4-44-444-400-4400000000000000−222222−2200000000000000000000
χ454-4-44-44-44004-4000004-4-4400000000000000000000000000000
χ464-4-44-44-44004-400000-444-400000000000000000000000000000
χ4788-8-800008-80000000000000000000000000000000000000000
χ4888-8-80000-880000000000000000000000000000000000000000
χ498-88-8000000000004i2−4i2000000000000000000000000000000000
χ508-88-800000000000−4i24i2000000000000000000000000000000000

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