Finite Group Databasebeta

← Group #150377

Character table — Group #150377

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order12222244444444444444444424444488888888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ7111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-1-1-1-1-1111111-1-1-1-1111-11-11-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-1-1-1111111-1-1-1-1111-11-11-111-1-1-1-111-1-111-1-111-1-111
χ11111111-1-1-1-1-1-1111111-1-1-1-111-111-1-11-1-11111-1-111-1-1-1-111-1-111
χ12111111-1-1-1-1-1-1111111-1-1-1-111-111-1-11-1-111-1-111-1-11111-1-111-1-1
χ13111111-1-1-1-1-1-1-1-111-1-11111-1-11-11-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-1-1-1-1-1-111-1-11111-1-11-11-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-222-2-200-2-20000000000000000000000
χ18222222222222-2-222-2-222-2-22200-2-20000000000000000000000
χ19222222-2-2-2-2-2-222222222-2-2-2-200-220000000000000000000000
χ20222222-2-2-2-2-2-2-2-222-2-2-2-2222200-220000000000000000000000
χ212-22-22-22i2i−2i−2i2i−2i002-2002-2002i−2i00000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ222-22-22-22i2i−2i−2i2i−2i002-2002-2002i−2i0000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ232-22-22-22i2i−2i−2i2i−2i002-200-2200−2i2i00000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ242-22-22-22i2i−2i−2i2i−2i002-200-2200−2i2i0000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ252-22-22-22i2i−2i−2i−2i2i2-2-222-2002i−2i000000000000000000002−2i2−i22−2i2−i2
χ262-22-22-22i2i−2i−2i−2i2i2-2-222-2002i−2i00000000000000000000−22−i2i2−22−i2i2
χ272-22-22-22i2i−2i−2i−2i2i-22-22-2200−2i2i00000000000000000000i2−i2−22−i2i22−2
χ282-22-22-22i2i−2i−2i−2i2i-22-22-2200−2i2i00000000000000000000−i2i22−2i2−i2−22
χ292-22-22-2−2i−2i2i2i2i−2i2-2-222-200−2i2i000000000000000000002−2−i2i22−2−i2i2
χ302-22-22-2−2i−2i2i2i2i−2i2-2-222-200−2i2i00000000000000000000−22i2−i2−22i2−i2
χ312-22-22-2−2i−2i2i2i2i−2i-22-22-22002i−2i00000000000000000000i2−i22−2−i2i2−22
χ322-22-22-2−2i−2i2i2i2i−2i-22-22-22002i−2i00000000000000000000−i2i2−22i2−i22−2
χ332-22-22-2−2i−2i2i2i−2i2i002-2002-200−2i2i00000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ342-22-22-2−2i−2i2i2i−2i2i002-2002-200−2i2i0000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ352-22-22-2−2i−2i2i2i−2i2i002-200-22002i−2i00000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ362-22-22-2−2i−2i2i2i−2i2i002-200-22002i−2i0000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ374444444444-4-400-4-40000000000000000000000000000000000
χ38444444-4-4-4-44400-4-40000000000000000000000000000000000
χ394444-4-44-44-4000000000000002200-2-200000000000000000000
χ404444-4-44-44-400000000000000-2-2002200000000000000000000
χ414444-4-4-44-44000000000000002-200-2200000000000000000000
χ424444-4-4-44-4400000000000000-22002-200000000000000000000
χ434-44-4-444i−4i−4i4i000000000000000000002i−2i2-20000000000000000
χ444-44-4-444i−4i−4i4i00000000000000000000−2i2i-220000000000000000
χ454-44-4-44−4i4i4i−4i000000000000000000002i−2i-220000000000000000
χ464-44-4-44−4i4i4i−4i00000000000000000000−2i2i2-20000000000000000
χ4788-8-8000000004-400-4400000000000000000000000000000000
χ4888-8-800000000-44004-400000000000000000000000000000000
χ498-8-88000000004400-4-400000000000000000000000000000000
χ508-8-8800000000-4-4004400000000000000000000000000000000

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