Finite Group Databasebeta

← Group #326656

Character table — Group #326656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12224444224444444444224444444488882444888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11-1-11-1-111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-111-1-111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-111111-1-11-1-1-1-111-1-11111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111-111-1-1-111-1-1-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-1-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-111111111-111-11111-1-1-1-1-1-111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ172222222222222222-2-2-2-20000-2-2000022-2-200000000002-20000000000
χ182222222222222222-2-2-2-20000-2-20000-2-2220000000000-220000000000
χ19222222222222-2-2-2-2-2-2-2-2000022000022-2-20000000000-220000000000
χ20222222222222-2-2-2-2-2-2-2-20000220000-2-22200000000002-20000000000
χ212222-2-2-2-222-2-2000022-2-200000022-2-22i−2i2i−2i00002i−2i0000000000000000
χ222222-2-2-2-222-2-2000022-2-200000022-2-2−2i2i−2i2i0000−2i2i0000000000000000
χ232222-2-2-2-222-2-2000022-2-2000000-2-2222i−2i2i−2i0000−2i2i0000000000000000
χ242222-2-2-2-222-2-2000022-2-2000000-2-222−2i2i−2i2i00002i−2i0000000000000000
χ252222-2-2-2-222-2-20000-2-22222-2-20000002i−2i−2i2i0000000000002i−2i00000000
χ262222-2-2-2-222-2-20000-2-22222-2-2000000−2i2i2i−2i000000000000−2i2i00000000
χ272222-2-2-2-222-2-20000-2-222-2-2220000002i−2i−2i2i000000000000−2i2i00000000
χ282222-2-2-2-222-2-20000-2-222-2-222000000−2i2i2i−2i0000000000002i−2i00000000
χ292222-2-2-2-2-2-2222i2i−2i−2i2-22-200002i−2i0000000002-2000002i−2i000000000000
χ302222-2-2-2-2-2-2222i2i−2i−2i2-22-200002i−2i000000000-2200000−2i2i000000000000
χ312222-2-2-2-2-2-2222i2i−2i−2i-22-220000−2i2i00000000200-2002i−2i00000000000000
χ322222-2-2-2-2-2-2222i2i−2i−2i-22-220000−2i2i00000000-200200−2i2i00000000000000
χ332222-2-2-2-2-2-222−2i−2i2i2i2-22-20000−2i2i0000000002-200000−2i2i000000000000
χ342222-2-2-2-2-2-222−2i−2i2i2i2-22-20000−2i2i000000000-22000002i−2i000000000000
χ352222-2-2-2-2-2-222−2i−2i2i2i-22-2200002i−2i00000000200-200−2i2i00000000000000
χ362222-2-2-2-2-2-222−2i−2i2i2i-22-2200002i−2i00000000-2002002i−2i00000000000000
χ3744444444-4-4-4-400004-4-44000000000000000000000000000000000000
χ3844444444-4-4-4-40000-444-4000000000000000000000000000000000000
χ3944-4-44i−4i4i−4i00002+2i−2−2i2−2i−2+2i00002-22i−2i002-22i−2i00000000000000000000000000
χ4044-4-44i−4i4i−4i00002+2i−2−2i2−2i−2+2i0000-22−2i2i00-22−2i2i00000000000000000000000000
χ4144-4-44i−4i4i−4i0000−2−2i2+2i−2+2i2−2i00002-22i−2i00-22−2i2i00000000000000000000000000
χ4244-4-44i−4i4i−4i0000−2−2i2+2i−2+2i2−2i0000-22−2i2i002-22i−2i00000000000000000000000000
χ4344-4-4−4i4i−4i4i00002−2i−2+2i2+2i−2−2i00002-2−2i2i002-2−2i2i00000000000000000000000000
χ4444-4-4−4i4i−4i4i00002−2i−2+2i2+2i−2−2i0000-222i−2i00-222i−2i00000000000000000000000000
χ4544-4-4−4i4i−4i4i0000−2+2i2−2i−2−2i2+2i00002-2−2i2i00-222i−2i00000000000000000000000000
χ4644-4-4−4i4i−4i4i0000−2+2i2−2i−2−2i2+2i0000-222i−2i002-2−2i2i00000000000000000000000000
χ474-4-4444-4-44-44-400000000000000000000000000000000000022−22000000
χ484-4-4444-4-44-44-4000000000000000000000000000000000000−2222000000
χ494-4-4444-4-4-44-440000000000000000000000000000000000000000002i2−2i2
χ504-4-4444-4-4-44-44000000000000000000000000000000000000000000−2i22i2
χ514-4-44-4-4444-4-44000000000000000000000000000000000000000022−2200
χ524-4-44-4-4444-4-440000000000000000000000000000000000000000−222200
χ534-4-44-4-444-444-40000000000000000000000000000000000000022−220000
χ544-4-44-4-444-444-400000000000000000000000000000000000000−22220000
χ558-88-88i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000

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