Finite Group Databasebeta

← Group #145859

Character table — Group #145859

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order1222224444444488888888888888884444888816161616161616164444
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-11-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-11-11-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ922222222222222-2-2-2-2-2-2-2-20000000000000000000000002-200
χ1022222222222222-2-2-2-2-2-2-2-2000000000000000000000000-2200
χ112222222222-2-2-2-2222-2-2-22-200000000020200-2-2000000000000
χ122222222222-2-2-2-2222-2-2-22-2000000000-20-20022000000000000
χ132222222222-2-2-2-2-2-2-2222-22000000002020-2-200000000000000
χ142222222222-2-2-2-2-2-2-2222-2200000000-20-202200000000000000
χ152222-2-22-22-2000000022-20-2i2i2i2i2−i2−i2−i2−i220-200000i2i2−i2−i200000000
χ162222-2-22-22-2000000022-20-2i2i2i2i2−i2−i2−i2−i2-20200000−i2−i2i2i200000000
χ172222-2-22-22-2000000022-20-2−i2−i2−i2−i2i2i2i2i220-200000−i2−i2i2i200000000
χ182222-2-22-22-2000000022-20-2−i2−i2−i2−i2i2i2i2i2-20200000i2i2−i2−i200000000
χ192222-2-2-22-22000022-2000-20i2i2−i2−i2i2i2−i2−i2020-200000000i2i2−i2−i20000
χ202222-2-2-22-22000022-2000-20i2i2−i2−i2i2i2−i2−i20-20200000000−i2−i2i2i20000
χ212222-2-2-22-22000022-2000-20−i2−i2i2i2−i2−i2i2i2020-200000000−i2−i2i2i20000
χ222222-2-2-22-22000022-2000-20−i2−i2i2i2−i2−i2i2i20-20200000000i2i2−i2−i20000
χ2322-2-22-222-2-222-2-22-222-2-2-22000000000000000000002-22-20000
χ2422-2-22-222-2-222-2-22-222-2-2-2200000000000000000000-22-220000
χ2522-2-22-222-2-222-2-2-22-2-2222-200000000000000002-22-200000000
χ2622-2-22-222-2-222-2-2-22-2-2222-20000000000000000-22-2200000000
χ2722-2-22-222-2-2-2-2222-22-222-2-22-22-22-22-200000000000000000000
χ2822-2-22-222-2-2-2-2222-22-222-2-2-22-22-22-2200000000000000000000
χ2922-2-22-222-2-2-2-222-22-22-2-222000000000000000000000000002i−2i
χ3022-2-22-222-2-2-2-222-22-22-2-22200000000000000000000000000−2i2i
χ3122-2-2-222-2-220000000-22-202i2−i2i2−i2−i2i2−i2i200002-200i2−i2−i2i200000000
χ3222-2-2-222-2-220000000-22-202i2−i2i2−i2−i2i2−i2i20000-2200−i2i2i2−i200000000
χ3322-2-2-222-2-220000000-22-202−i2i2−i2i2i2−i2i2−i200002-200−i2i2i2−i200000000
χ3422-2-2-222-2-220000000-22-202−i2i2−i2i2i2−i2i2−i20000-2200i2−i2−i2i200000000
χ3522-2-2-22-222-200002-2-200020i2−i2−i2i2i2−i2−i2i20000002-20000i2−i2−i2i20000
χ3622-2-2-22-222-200002-2-200020i2−i2−i2i2i2−i2−i2i2000000-220000−i2i2i2−i20000
χ3722-2-2-22-222-200002-2-200020−i2i2i2−i2−i2i2i2−i20000002-20000−i2i2i2−i20000
χ3822-2-2-22-222-200002-2-200020−i2i2i2−i2−i2i2i2−i2000000-220000i2−i2−i2i20000
χ39444444-4-4-4-400000000000022-2-2-2-22200000000000000000000
χ40444444-4-4-4-4000000000000-2-22222-2-200000000000000000000
χ414444-4-44-44-40000000-4-44040000000000000000000000000000
χ424444-4-4-44-440000-4-44000400000000000000000000000000000
χ4344-4-44-4-4-4440000000000002-2-22-222-200000000000000000000
χ4444-4-44-4-4-444000000000000-222-22-2-2200000000000000000000
χ4544-4-4-444-4-4400000004-440-40000000000000000000000000000
χ4644-4-4-44-444-40000-444000-400000000000000000000000000000
χ478-88-80000004-44-4000000000000000000000000000000000000
χ488-88-8000000-44-44000000000000000000000000000000000000
χ498-8-880000004-4-44000000000000000000000000000000000000
χ508-8-88000000-444-4000000000000000000000000000000000000

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