Finite Group Databasebeta

← Group #138221

Character table — Group #138221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order122222444444448888888824448888161616161616161616161616161616164444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011111111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ1211111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ172222222222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000000000
χ212-2-222-22-22-20000002-2002-2002i−2i2i−2i00i2−i2i2−i22−22−2000000000000
χ222-2-222-22-22-20000002-2002-2002i−2i2i−2i00−i2i2−i2i2−22−22000000000000
χ232-2-222-22-22-20000002-2002-200−2i2i−2i2i00i2−i2i2−i2−22−22000000000000
χ242-2-222-22-22-20000002-2002-200−2i2i−2i2i00−i2i2−i2i22−22−2000000000000
χ252-2-222-22-22-2000000-2200-22002i−2i−2i2i002−2−22−i2i2i2−i2000000000000
χ262-2-222-22-22-2000000-2200-22002i−2i−2i2i00−222−2i2−i2−i2i2000000000000
χ272-2-222-22-22-2000000-2200-2200−2i2i2i−2i002−2−22i2−i2−i2i2000000000000
χ282-2-222-22-22-2000000-2200-2200−2i2i2i−2i00−222−2−i2i2i2−i2000000000000
χ292-2-22-22-2-22222-2-22-2222-2-2-200000000000000002i−2i2i−2i00000000
χ302-2-22-22-2-22222-2-22-2222-2-2-20000000000000000−2i2i−2i2i00000000
χ312-2-22-22-2-22222-2-2-22-2-2-222200000000000000002-2-2200000000
χ322-2-22-22-2-22222-2-2-22-2-2-22220000000000000000-222-200000000
χ332-2-22-22-2-222-2-2222-2-2-22-222000000000000000000002-22-20000
χ342-2-22-22-2-222-2-2222-2-2-22-22200000000000000000000-22-220000
χ352-2-22-22-2-222-2-222-2222-22-2-2000000000000000000002i−2i−2i2i0000
χ362-2-22-22-2-222-2-222-2222-22-2-200000000000000000000−2i2i2i−2i0000
χ37444444-4-4-4-40000000000004-400000000000000000000000000
χ38444444-4-4-4-4000000000000-4400000000000000000000000000
χ394444-4-44-4-4400004-400-44000000000000000000000000000000
χ404444-4-44-4-440000-44004-4000000000000000000000000000000
χ414444-4-4-444-40000004-400-440000000000000000000000000000
χ424444-4-4-444-4000000-44004-40000000000000000000000000000
χ434-4-444-4-44-4400004400-4-4000000000000000000000000000000
χ444-4-444-4-44-440000-4-40044000000000000000000000000000000
χ454-4-44-4444-4-40000000000000000004i−4i00000000000000000000
χ464-4-44-4444-4-4000000000000000000−4i4i00000000000000000000
χ4788-8-80000004-44-4000000000000000000000000000000000000
χ4888-8-8000000-44-44000000000000000000000000000000000000
χ498-88-80000004-4-44000000000000000000000000000000000000
χ508-88-8000000-444-4000000000000000000000000000000000000

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