Finite Group Databasebeta

← Group #140949

Character table — Group #140949

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222-2-2-2-2222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-22222-2-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-2222-2-2-2-22-2-2-2-22222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-22222-222-2-222-2-2000000000000000000000000
χ212-2222-2-2-22-22-200000002i2i−2i−2i02-2002i−2i0000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ222-2222-2-2-22-22-200000002i2i−2i−2i02-2002i−2i000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ232-2222-2-2-22-22-200000002i2i−2i−2i0-2200−2i2i0000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ242-2222-2-2-22-22-200000002i2i−2i−2i0-2200−2i2i000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ252-2222-2-2-22-22-20000000−2i−2i2i2i02-200−2i2i0000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ262-2222-2-2-22-22-20000000−2i−2i2i2i02-200−2i2i000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ272-2222-2-2-22-22-20000000−2i−2i2i2i0-22002i−2i0000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ282-2222-2-2-22-22-20000000−2i−2i2i2i0-22002i−2i000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ292-22-2-222-2-2-222000022-22-22-2-2002-2000000000000002i−2i002i−2i00000000
χ302-22-2-222-2-2-222000022-22-22-2-2002-200000000000000−2i2i00−2i2i00000000
χ312-22-2-222-2-2-222000022-2-22-22-200-220000000000002i−2i002i−2i0000000000
χ322-22-2-222-2-2-222000022-2-22-22-200-22000000000000−2i2i00−2i2i0000000000
χ332-22-2-222-2-2-2220000-2-222-22-2200-220000000000002-200-220000000000
χ342-22-2-222-2-2-2220000-2-222-22-2200-22000000000000-22002-20000000000
χ352-22-2-222-2-2-2220000-2-22-22-222002-2000000000000002-200-2200000000
χ362-22-2-222-2-2-2220000-2-22-22-222002-200000000000000-22002-200000000
χ3744444444-4-4-4-444-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4-4-4440000000000000000000000000000000000000000
χ39444-4-4-4-444-4-4400004-440000-400000000000000000000000000000000
χ40444-4-4-4-444-4-440000-44-40000400000000000000000000000000000000
χ41444-4-4-4-44-444-400000004i−4i−4i4i000000000000000000000000000000000
χ42444-4-4-4-44-444-40000000−4i4i4i−4i000000000000000000000000000000000
χ4344-44-44-4-40000004-4000000000000000000002i−2i2i−2i0000000000000000
χ4444-44-44-4-40000004-400000000000000000000−2i2i−2i2i0000000000000000
χ4544-44-44-4-4000000-44000000000000000000002i−2i−2i2i0000000000000000
χ4644-44-44-4-4000000-4400000000000000000000−2i2i2i−2i0000000000000000
χ4744-4-44-44-400004i−4i0000000000000000002-22i−2i00000000000000000000
χ4844-4-44-44-400004i−4i000000000000000000-22−2i2i00000000000000000000
χ4944-4-44-44-40000−4i4i0000000000000000002-2−2i2i00000000000000000000
χ5044-4-44-44-40000−4i4i000000000000000000-222i−2i00000000000000000000
χ514-4444-4-4-4-44-4400004-4-40000400000000000000000000000000000000
χ524-4444-4-4-4-44-440000-4440000-400000000000000000000000000000000
χ534-44-4-444-444-4-40000000000000000004i−4i000000000000000000000000
χ544-44-4-444-444-4-4000000000000000000−4i4i000000000000000000000000
χ558-8-88-8-888000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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