Finite Group Databasebeta

← Group #103975

Character table — Group #103975

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222444444444444444488888888224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ922222222222222-2-2-2-2-2-222-2-20000000000000000000022-2-200000000
χ1022222222222222-2-2-2-2-2-222-2-200000000000000000000-2-22200000000
χ11222222222222-2-2222-2-2-2-2-22-2000000000000000022-2-2000000000000
χ12222222222222-2-2222-2-2-2-2-22-20000000000000000-2-222000000000000
χ13222222222222-2-2-2-2-2222-2-2-220000000022-2-200000000000000000000
χ14222222222222-2-2-2-2-2222-2-2-2200000000-2-22200000000000000000000
χ1522222222-2-2-2-22222-222-2-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ1622222222-2-2-2-22222-222-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ1722222222-2-2-2-222-2-22-2-22-2-22200000000000022-2-20000000000000000
χ1822222222-2-2-2-222-2-22-2-22-2-222000000000000-2-2220000000000000000
χ1922222222-2-2-2-2-2-222-2-2-2222-22000000000000000000000000000022-2-2
χ2022222222-2-2-2-2-2-222-2-2-2222-220000000000000000000000000000-2-222
χ2122222222-2-2-2-2-2-2-2-2222-2222-200000000000000000000000022-2-20000
χ2222222222-2-2-2-2-2-2-2-2222-2222-2000000000000000000000000-2-2220000
χ2322-222-2-2-222-2-2000002-2-20002i2i2−i2−i2i2i2−i2−i22-200000000000000i2−i2i2−i20000
χ2422-222-2-2-222-2-2000002-2-20002i2i2−i2−i2i2i2−i2−i2-2200000000000000−i2i2−i2i20000
χ2522-222-2-2-222-2-2000002-2-20002−i2−i2i2i2−i2−i2i2i22-200000000000000−i2i2−i2i20000
χ2622-222-2-2-222-2-2000002-2-20002−i2−i2i2i2−i2−i2i2i2-2200000000000000i2−i2i2−i20000
χ2722-222-2-2-2-2-222000002-22000-222−2−2−2−222002i−2i000000000000i2−i2−i2i20000
χ2822-222-2-2-2-2-222000002-22000-222−2−2−2−22200−2i2i000000000000−i2i2i2−i20000
χ2922-222-2-2-2-2-222000002-22000-2−2−22222−2−2002i−2i000000000000−i2i2i2−i20000
χ3022-222-2-2-2-2-222000002-22000-2−2−22222−2−200−2i2i000000000000i2−i2−i2i20000
χ3122-2-2-222-22-22-2002-2-200000202−22−22−22−200000000002i−2i00000000i2−i2i2−i2
χ3222-2-2-222-22-22-2002-2-200000202−22−22−22−20000000000−2i2i00000000−i2i2−i2i2
χ3322-2-2-222-22-22-2002-2-20000020−22−22−22−2200000000002i−2i00000000−i2i2−i2i2
χ3422-2-2-222-22-22-2002-2-20000020−22−22−22−220000000000−2i2i00000000i2−i2i2−i2
χ3522-2-2-222-2-22-22002-2200000-20i2−i2i2−i2−i2i2−i2i2000000002-20000000000i2−i2−i2i2
χ3622-2-2-222-2-22-22002-2200000-20i2−i2i2−i2−i2i2−i2i200000000-220000000000−i2i2i2−i2
χ3722-2-2-222-2-22-22002-2200000-20−i2i2−i2i2i2−i2i2−i2000000002-20000000000−i2i2i2−i2
χ3822-2-2-222-2-22-22002-2200000-20−i2i2−i2i2i2−i2i2−i200000000-220000000000i2−i2−i2i2
χ39444-4-4-4-444-4-440000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ40444-4-4-4-444-4-44000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ41444-4-4-4-44-444-40000000000002-2-22-222-2000000000000000000000000
χ42444-4-4-4-44-444-4000000000000-222-22-2-22000000000000000000000000
χ4344-444-4-4-444-4-400000-444000-400000000000000000000000000000000
χ4444-444-4-4-4-4-44400000-44-4000400000000000000000000000000000000
χ4544-4-4-444-44-44-400-44400000-4000000000000000000000000000000000
χ4644-4-4-444-4-44-4400-44-4000004000000000000000000000000000000000
χ474-444-44-4-40000000000004i−4i000000000000002-22i−2i0000000000000000
χ484-444-44-4-40000000000004i−4i00000000000000-22−2i2i0000000000000000
χ494-444-44-4-4000000000000−4i4i000000000000002-2−2i2i0000000000000000
χ504-444-44-4-4000000000000−4i4i00000000000000-222i−2i0000000000000000
χ514-44-44-44-400004-4000000000000000000000000000000002i2−2i200000000
χ524-44-44-44-400004-400000000000000000000000000000000−2i22i200000000
χ534-44-44-44-40000-440000000000000000000000000000002i2−2i20000000000
χ544-44-44-44-40000-44000000000000000000000000000000−2i22i20000000000
χ558-8-88-8-888000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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