Finite Group Databasebeta

← Group #272589

Character table — Group #272589

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222244444488888888888888816161616161616161616161616161616323232
order12224444442444442244444888888882444448888888888488
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11111-11-1-11-1111-1-1-1-1-111-1-1-1
χ311111111111111111111111-1-111-1-1-1-1111111-1-1-1111-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-111-1-1111
χ511111111111111111-11-1-11-111111111-1-1-1-1-1-11-1-111111-1-1-1-11
χ611111111111111111-11-1-11-111-1-111111-111-111-1-1-1-1-1-1-1-1-111-1
χ711111111111111111-11-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1
χ811111111111111111-11-1-11-1-1-1-1-1-1-1-1-11-111-11-111-1-1-11111-1-11
χ911111111111-1-1111-11-111-111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-11-11
χ1011111111111-1-1111-11-111-1111-1-1-1-1-1-1-1-111-1-1111-11111-1-1-11-1
χ1111111111111-1-1111-11-111-11-1-11111111-1-1-1-11-1-1-11-1-11111-11-1
χ1211111111111-1-1111-11-111-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-1111-11
χ1311111111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1-11111-11-1-11-1-1-1-111-111
χ1411111111111-1-1111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111-1-1-11111111-1-1
χ1511111111111-1-1111-1-1-1-1-1-1-1-1-1111111-11111-1-1111-1-111-1-11-1-1
χ1611111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-111-1-1-1-1-111
χ172222222-2-22-222-2-2220-200-20220022-2-2000000-2000000000000
χ182222222-2-22-222-2-2220-200-20-2-200-2-2220000002000000000000
χ192222222-2-22-2-2-2-2-22-20200202200-2-222000000-2000000000000
χ202222222-2-22-2-2-2-2-22-2020020-2-20022-2-20000002000000000000
χ2122222-2222-2-222-22-2-22-2-2-222000000000200-200000000000000
χ2222222-2222-2-222-22-2-2-2-2222-2000000000-200200000000000000
χ2322222-2222-2-2-2-2-22-2222-2-2-22000000000-200200000000000000
χ2422222-2222-2-2-2-2-22-22-2222-2-2000000000200-200000000000000
χ2522222-22-2-2-22222-2-2-20200-200000000000000002i−2i000002i−2i000
χ2622222-22-2-2-22222-2-2-20200-20000000000000000−2i2i00000−2i2i000
χ2722222-22-2-2-22-2-22-2-220-200200000000000000002i−2i00000−2i2i000
χ2822222-22-2-2-22-2-22-2-220-20020000000000000000−2i2i000002i−2i000
χ292222-22-2222-2002-2-2020-220-200220000-200002000-2000000000
χ302222-22-2222-2002-2-2020-220-200-2-2000020000-20002000000000
χ312222-22-2222-2002-2-20-202-2020022000020000-2000-2000000000
χ322222-22-2222-2002-2-20-202-20200-2-20000-2000020002000000000
χ332222-2-2-222-2200-2-220202-20-200000000002-20000002-20000000
χ342222-2-2-222-2200-2-220202-20-20000000000-22000000-220000000
χ352222-2-2-222-2200-2-220-20-220200000000002-2000000-220000000
χ362222-2-2-222-2200-2-220-20-22020000000000-220000002-20000000
χ374444-44-4-4-44400-44-40000000000000000000000000000000000
χ384444-4-4-4-4-4-4-4004440000000000000000000000000000000000
χ394-44-40-400040000000000000002i2−2i2002i2−2i20000000000002-200000
χ404-44-40-400040000000000000002i2−2i200−2i22i2000000000000-2200000
χ414-44-40-40004000000000000000−2i22i2002i2−2i2000000000000-2200000
χ424-44-40-40004000000000000000−2i22i200−2i22i20000000000002-200000
χ434-4-4440-400004i−4i000000000022−22002i2−2i2000000000000000000000
χ444-4-4440-400004i−4i0000000000−222200−2i22i2000000000000000000000
χ454-4-4440-40000−4i4i000000000022−2200−2i22i2000000000000000000000
χ464-4-4440-40000−4i4i0000000000−2222002i2−2i2000000000000000000000
χ4788-8-80008-800000000000000000000000000000000000000000
χ4888-8-8000-8800000000000000000000000000000000000000000
χ498-88-808000-80000000000000000000000000000000000000000
χ508-8-88-8080000000000000000000000000000000000000000000

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