Finite Group Databasebeta

← Group #150324

Character table — Group #150324

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order12222244444444444444444422444488888888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-11-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-111-1-1-1-1-1-1-1-11-11-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-111-1-1-1-1-1-1-1-11-11-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-1-1-1-1-1111111-1-1-1-111-1111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-1-1-1111111-1-1-1-111-1111-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111-1-1-1-1-1-1111111-1-1-1-111-1-11-111-1-11111-1-111-1-1-1-111-1-111
χ12111111-1-1-1-1-1-1111111-1-1-1-111-1-11-111-1-111-1-111-1-11111-1-111-1-1
χ13111111-1-1-1-1-1-1-1-111-1-11111-1-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-1-1-1-1-1-111-1-11111-1-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-222-2-2-20-200000000000000000000000
χ18222222222222-2-222-2-222-2-222-20-200000000000000000000000
χ19222222-2-2-2-2-2-222222222-2-2-2-220-200000000000000000000000
χ20222222-2-2-2-2-2-2-2-222-2-2-2-2222220-200000000000000000000000
χ2122-2-22-22i2i−2i−2i2i−2i002-2002i−2i002-20000000000i2−i22−2i2−i22−200000000
χ2222-2-22-22i2i−2i−2i2i−2i002-2002i−2i002-20000000000−i2i2−22−i2i2−2200000000
χ2322-2-22-22i2i−2i−2i2i−2i002-200−2i2i00-2200000000002−2−i2i2−22i2−i200000000
χ2422-2-22-22i2i−2i−2i2i−2i002-200−2i2i00-220000000000−22i2−i22−2−i2i200000000
χ2522-2-22-22i2i−2i−2i−2i2i2i−2i-222i−2i002-2000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ2622-2-22-22i2i−2i−2i−2i2i2i−2i-222i−2i002-200000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ2722-2-22-22i2i−2i−2i−2i2i−2i2i-22−2i2i00-22000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ2822-2-22-22i2i−2i−2i−2i2i−2i2i-22−2i2i00-2200000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ2922-2-22-2−2i−2i2i2i2i−2i2i−2i-222i−2i00-22000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ3022-2-22-2−2i−2i2i2i2i−2i2i−2i-222i−2i00-2200000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ3122-2-22-2−2i−2i2i2i2i−2i−2i2i-22−2i2i002-2000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ3222-2-22-2−2i−2i2i2i2i−2i−2i2i-22−2i2i002-200000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ3322-2-22-2−2i−2i2i2i−2i2i002-2002i−2i00-2200000000002−2i2−i2−22−i2i200000000
χ3422-2-22-2−2i−2i2i2i−2i2i002-2002i−2i00-220000000000−22−i2i22−2i2−i200000000
χ3522-2-22-2−2i−2i2i2i−2i2i002-200−2i2i002-20000000000i2−i2−22i2−i2−2200000000
χ3622-2-22-2−2i−2i2i2i−2i2i002-200−2i2i002-20000000000−i2i22−2−i2i22−200000000
χ374444444444-4-400-4-40000000000000000000000000000000000
χ38444444-4-4-4-44400-4-40000000000000000000000000000000000
χ394444-4-44-44-400000000000000020-22-200000000000000000000
χ404444-4-44-44-4000000000000000-202-2200000000000000000000
χ414444-4-4-44-4400000000000000020-2-2200000000000000000000
χ424444-4-4-44-44000000000000000-2022-200000000000000000000
χ4344-4-4-444i−4i−4i4i000000000000000000002-22i−2i0000000000000000
χ4444-4-4-444i−4i−4i4i00000000000000000000-22−2i2i0000000000000000
χ4544-4-4-44−4i4i4i−4i000000000000000000002-2−2i2i0000000000000000
χ4644-4-4-44−4i4i4i−4i00000000000000000000-222i−2i0000000000000000
χ478-88-8000000004i−4i00−4i4i00000000000000000000000000000000
χ488-88-800000000−4i4i004i−4i00000000000000000000000000000000
χ498-8-88000000004400-4-400000000000000000000000000000000
χ508-8-8800000000-4-4004400000000000000000000000000000000

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