Finite Group Databasebeta

← Group #150331

Character table — Group #150331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224444442222444444448888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2220000000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-20000000000000000000000000000
χ192222-2-2-2-222-2-2-2-2222222-2-2-2-222-2-20000000000000000000000000000
χ202222-2-2-2-222-2-2-2-222-2-2-2-222-2-222220000000000000000000000000000
χ2122-2-22i2i−2i−2i2-22i−2i2i−2i2-2002-22i−2i000000000000000000000000002−2i2−i2i2−i22−2
χ2222-2-22i2i−2i−2i2-22i−2i2i−2i2-2002-22i−2i00000000000000000000000000−22−i2i2−i2i2−22
χ2322-2-22i2i−2i−2i2-22i−2i2i−2i2-200-22−2i2i00000000000000000000000000i2−i2−222−2−i2i2
χ2422-2-22i2i−2i−2i2-22i−2i2i−2i2-200-22−2i2i00000000000000000000000000−i2i22−2−22i2−i2
χ2522-2-22i2i−2i−2i2-22i−2i−2i2i-222-2000000002i−2i0000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ2622-2-22i2i−2i−2i2-22i−2i−2i2i-222-2000000002i−2i000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ2722-2-22i2i−2i−2i2-22i−2i−2i2i-22-2200000000−2i2i0000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00000000
χ2822-2-22i2i−2i−2i2-22i−2i−2i2i-22-2200000000−2i2i000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00000000
χ2922-2-2−2i−2i2i2i2-2−2i2i2i−2i-222-200000000−2i2i0000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ3022-2-2−2i−2i2i2i2-2−2i2i2i−2i-222-200000000−2i2i000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ3122-2-2−2i−2i2i2i2-2−2i2i2i−2i-22-22000000002i−2i0000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00000000
χ3222-2-2−2i−2i2i2i2-2−2i2i2i−2i-22-22000000002i−2i000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00000000
χ3322-2-2−2i−2i2i2i2-2−2i2i−2i2i2-2002-2−2i2i000000000000000000000000002−2−i2i2−i2i22−2
χ3422-2-2−2i−2i2i2i2-2−2i2i−2i2i2-2002-2−2i2i00000000000000000000000000−22i2−i2i2−i2−22
χ3522-2-2−2i−2i2i2i2-2−2i2i−2i2i2-200-222i−2i00000000000000000000000000i2−i22−2−22−i2i2
χ3622-2-2−2i−2i2i2i2-2−2i2i−2i2i2-200-222i−2i00000000000000000000000000−i2i2−222−2i2−i2
χ37444444444444-4-4-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4000000000000000022-2-222-2-200000000000000000000
χ3944444444-4-4-4-40000000000000000-2-222-2-22200000000000000000000
χ404444-4-4-4-444-4-444-4-40000000000000000000000000000000000000000
χ414444-4-4-4-4-4-444000000000000000022-2-2-2-22200000000000000000000
χ424444-4-4-4-4-4-4440000000000000000-2-22222-2-200000000000000000000
χ4344-4-44i4i−4i−4i-44−4i4i0000000000000000000000002i−2i2-20000000000000000
χ4444-4-44i4i−4i−4i-44−4i4i000000000000000000000000−2i2i-220000000000000000
χ4544-4-4−4i−4i4i4i-444i−4i0000000000000000000000002i−2i-220000000000000000
χ4644-4-4−4i−4i4i4i-444i−4i000000000000000000000000−2i2i2-20000000000000000
χ474-44-44-44-4000000000000002-22-200002i2−2i2002i2−2i200000000000000000000
χ484-44-44-44-4000000000000002-22-20000−2i22i200−2i22i200000000000000000000
χ494-44-44-44-400000000000000-22-22002i2−2i2002i2−2i20000000000000000000000
χ504-44-44-44-400000000000000-22-2200−2i22i200−2i22i20000000000000000000000
χ514-44-4-44-44000000000000002-2-2200002i2−2i200−2i22i200000000000000000000
χ524-44-4-44-44000000000000002-2-220000−2i22i2002i2−2i200000000000000000000
χ534-44-4-44-4400000000000000-222-2002i2−2i200−2i22i20000000000000000000000
χ544-44-4-44-4400000000000000-222-200−2i22i2002i2−2i20000000000000000000000
χ558-8-888i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000

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