Finite Group Databasebeta

← Group #150211

Character table — Group #150211

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order12222244442244224444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ611111111111111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ711111111111111-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii
χ811111111111111-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i
χ9111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111
χ11111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-1-111-1-111
χ12111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ14111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ15111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ16111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ172222222222222222-2-222-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-222000000000000000000000000
χ19222222-2-2-2-2-2-2222222-2-2-2-222-2-2000000000000000000000000
χ20222222-2-2-2-2-2-222-2-2-2-222-2-22222000000000000000000000000
χ212-2-22-2222-2-22-22-2002i−2i0000002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ222-2-22-2222-2-22-22-2002i−2i0000002i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ232-2-22-2222-2-22-22-200−2i2i000000−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ242-2-22-2222-2-22-22-200−2i2i000000−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ252-2-22-2222-2-2-22-222-2002-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ262-2-22-2222-2-2-22-222-2002-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ272-2-22-2222-2-2-22-22-2200-2200000000000000000000002−22−2−22−22
χ282-2-22-2222-2-2-22-22-2200-220000000000000000000000−22−222−22−2
χ292-2-22-22-2-2222-2-222-200-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ302-2-22-22-2-2222-2-222-200-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ312-2-22-22-2-2222-2-22-22002-200000000000000000000002−2−22−222−2
χ322-2-22-22-2-2222-2-22-22002-20000000000000000000000−222−22−2−22
χ332-2-22-22-2-222-222-2002i−2i000000−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ342-2-22-22-2-222-222-2002i−2i000000−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ352-2-22-22-2-222-222-200−2i2i0000002i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ362-2-22-22-2-222-222-200−2i2i0000002i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ374444444444-4-4-4-4000000000000000000000000000000000000
χ38444444-4-4-4-444-4-4000000000000000000000000000000000000
χ394444-4-44-44-400000000000000000000000000002i−2i2i−2i00000000
χ404444-4-44-44-40000000000000000000000000000−2i2i−2i2i00000000
χ414444-4-4-44-4400000000000000000000000000002i−2i−2i2i00000000
χ424444-4-4-44-440000000000000000000000000000−2i2i2i−2i00000000
χ434-4-444-44-4-4400000000000000002i−2i2i−2i00000000000000000000
χ444-4-444-44-4-440000000000000000−2i2i−2i2i00000000000000000000
χ454-4-444-4-444-400000000000000002i−2i−2i2i00000000000000000000
χ464-4-444-4-444-40000000000000000−2i2i2i−2i00000000000000000000
χ4788-8-800000000000000004i−4i0000000000000000000000000000
χ4888-8-80000000000000000−4i4i0000000000000000000000000000
χ498-88-80000000000000000004i−4i00000000000000000000000000
χ508-88-8000000000000000000−4i4i00000000000000000000000000

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