Finite Group Databasebeta

← Group #150321

Character table — Group #150321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order12222244444444444422444424444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111-1-111-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii
χ8111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i
χ9111111-1-1-1-1-1-111111111-1-1-1-111-11-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-1-1-111111111-1-1-1-111-11-1-1-1-111-1-11111-1-1-1-111-1-111
χ11111111-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-111-1-1-1-111-1-111-1-111
χ12111111-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ14111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ15111111-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ16111111-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2220-2-200000000000000000000000
χ18222222222222-2-222-2-22222-2-20-2-200000000000000000000000
χ19222222-2-2-2-2-2-2222222-2-222-2-20-2200000000000000000000000
χ20222222-2-2-2-2-2-2-2-222-2-222-2-2220-2200000000000000000000000
χ2122-2-22-22i2i−2i−2i2i−2i002-2002-22i−2i000000000000000000002−2i2−i22−2i2−i2
χ2222-2-22-22i2i−2i−2i2i−2i002-2002-22i−2i00000000000000000000−22−i2i2−22−i2i2
χ2322-2-22-22i2i−2i−2i2i−2i002-200-22−2i2i00000000000000000000i2−i2−22−i2i22−2
χ2422-2-22-22i2i−2i−2i2i−2i002-200-22−2i2i00000000000000000000−i2i22−2i2−i2−22
χ2522-2-22-22i2i−2i−2i−2i2i2i−2i-222i−2i00002-20000001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ2622-2-22-22i2i−2i−2i−2i2i2i−2i-222i−2i00002-2000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ2722-2-22-22i2i−2i−2i−2i2i−2i2i-22−2i2i0000-220000001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000
χ2822-2-22-22i2i−2i−2i−2i2i−2i2i-22−2i2i0000-22000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000
χ2922-2-22-2−2i−2i2i2i2i−2i2i−2i-222i−2i0000-220000001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000
χ3022-2-22-2−2i−2i2i2i2i−2i2i−2i-222i−2i0000-22000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000
χ3122-2-22-2−2i−2i2i2i2i−2i−2i2i-22−2i2i00002-20000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ3222-2-22-2−2i−2i2i2i2i−2i−2i2i-22−2i2i00002-2000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ3322-2-22-2−2i−2i2i2i−2i2i002-2002-2−2i2i000000000000000000002−2−i2i22−2−i2i2
χ3422-2-22-2−2i−2i2i2i−2i2i002-2002-2−2i2i00000000000000000000−22i2−i2−22i2−i2
χ3522-2-22-2−2i−2i2i2i−2i2i002-200-222i−2i00000000000000000000i2−i22−2−i2i2−22
χ3622-2-22-2−2i−2i2i2i−2i2i002-200-222i−2i00000000000000000000−i2i2−22i2−i22−2
χ374444444444-4-400-4-40000000000000000000000000000000000
χ38444444-4-4-4-44400-4-40000000000000000000000000000000000
χ394444-4-44-44-400000000000000200-22-200000000000000000000
χ404444-4-44-44-400000000000000-2002-2200000000000000000000
χ414444-4-4-44-4400000000000000200-2-2200000000000000000000
χ424444-4-4-44-4400000000000000-20022-200000000000000000000
χ4344-4-4-444i−4i−4i4i00000000000000000000000000002-22i−2i00000000
χ4444-4-4-444i−4i−4i4i0000000000000000000000000000-22−2i2i00000000
χ4544-4-4-44−4i4i4i−4i00000000000000000000000000002-2−2i2i00000000
χ4644-4-4-44−4i4i4i−4i0000000000000000000000000000-222i−2i00000000
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).