Finite Group Databasebeta

← Group #252010

Character table — Group #252010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222224444444444444424444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111-1-1-1-111-1-11-111-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111-1-1-1-111-1-11-111-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111-1-1-1-11-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1
χ81111111111111111111-1-1-1-11-1-1-1-11-1-1111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1111111-11111-11-1-1-111-11-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111-11111-11-1-1-111-11-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111-11111-1-1-1-11-1-11-11111-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-1111111-11111-1-1-1-11-1-11-111-1-11111-1-111-1-1-1-111
χ1311111111-1-1-1-1111111-1-1-1-1-1-1111-1-11-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-1111111-1-1-1-1-1-1111-1-11-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-1111111-1-1-1-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-11111-1-1-1-11111-1-1
χ17222222222222-2-2-222-2-20000-220020-2-20000000000000000000
χ18222222222222-2-2-222-2-20000-2-200-20220000000000000000000
χ192222222222-2-22-2-2-2-22-222-2-2202-200000000000000000000000
χ202222222222-2-22-2-2-2-22-2-2-22220-2200000000000000000000000
χ212222222222-2-2-222-2-2-220000-20000200-22-20000000000000000
χ222222222222-2-2-222-2-2-220000-20000-2002-220000000000000000
χ2322222222-2-2222-2-2-2-22222-2-2-20-2200000000000000000000000
χ2422222222-2-2222-2-2-2-222-2-222-202-200000000000000000000000
χ2522222222-2-222-222-2-2-2-2000020000200-2-220000000000000000
χ2622222222-2-222-222-2-2-2-2000020000-20022-20000000000000000
χ2722222222-2-2-2-2-2-2-222-2200002200-20-220000000000000000000
χ2822222222-2-2-2-2-2-2-222-2200002-200202-20000000000000000000
χ2922-2-2-22-22000022-22-2-202i−2i2i−2i00000000000002-200000000002i−2i
χ3022-2-2-22-22000022-22-2-202i−2i2i−2i0000000000000-220000000000−2i2i
χ3122-2-2-22-22000022-22-2-20−2i2i−2i2i00000000000002-20000000000−2i2i
χ3222-2-2-22-22000022-22-2-20−2i2i−2i2i0000000000000-2200000000002i−2i
χ3322-2-2-22-2200002-22-22-202i−2i−2i2i000000000002-200000000002i−2i00
χ3422-2-2-22-2200002-22-22-202i−2i−2i2i00000000000-220000000000−2i2i00
χ3522-2-2-22-2200002-22-22-20−2i2i2i−2i000000000002-20000000000−2i2i00
χ3622-2-2-22-2200002-22-22-20−2i2i2i−2i00000000000-2200000000002i−2i00
χ374444-4-4-4-44-4000000000000000000000000000000002-22-20000
χ384444-4-4-4-44-400000000000000000000000000000000-22-220000
χ394444-4-4-4-4-44000000000000000000000000000000002-2-220000
χ404444-4-4-4-4-4400000000000000000000000000000000-222-20000
χ4144-4-4-44-440000-44-4-44400000000000000000000000000000000
χ4244-4-4-44-440000-4-444-4400000000000000000000000000000000
χ434-4-44-444-4004-4000000000000000000000000002i−2i2i−2i00000000
χ444-4-44-444-4004-400000000000000000000000000−2i2i−2i2i00000000
χ454-4-44-444-400-44000000000000000000000000002i−2i−2i2i00000000
χ464-4-44-444-400-4400000000000000000000000000−2i2i2i−2i00000000
χ4788-8-88-88-8000000000000000000000000000000000000000000
χ488-88-888-8-8000000000000000000000000000000000000000000
χ498-88-8-8-888000000000000000000000000000000000000000000
χ508-8-888-8-88000000000000000000000000000000000000000000

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