Finite Group Databasebeta

← Group #119875

Character table — Group #119875

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444448888888888888888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111-1-1-11-11111-1-1-111-1-1-1111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111-1-1-11-11111-1-1-111-1-1-1111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111-1-1-11-11111-1-1-111-1-1-1111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111-1-1-11-11111-1-1-111-1-1-1111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111-1-1-11-11111-1-1-111-1-1-1111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i
χ1411111-1-1-11-11111-1-1-111-1-1-1111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii
χ1511111-1-1-11-11111-1-1-111-1-1-1111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii
χ1611111-1-1-11-11111-1-1-111-1-1-1111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i
χ17222222222222222-2-2-2-2222-2-2-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-200000000-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-2-222-2-2-2-2-222-22-2-20000000000000000000000000000000000002i−2i2i−2i
χ202222222222-2-2-2-2-222-2-2-2-2-222-22-2-2000000000000000000000000000000000000−2i2i−2i2i
χ212222222222-2-2-2-2-2-2-222-2-2-2-2-22-2220000000000000000000000002-22-2000000000000
χ222222222222-2-2-2-2-2-2-222-2-2-2-2-22-222000000000000000000000000-22-22000000000000
χ2322222-2-2-22-22222-222-2-2-2-2-2-2-2-2222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2422222-2-2-22-22222-222-2-2-2-2-2-2-2-222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2522222-2-2-22-2-2-2-2-222222222-2-222-2-20000000000000000000000002-2-22000000000000
χ2622222-2-2-22-2-2-2-2-222222222-2-222-2-2000000000000000000000000-222-2000000000000
χ2722222-2-2-22-2-2-2-2-22-2-2-2-222222-2-2220000000000000000000000000000000000002-2-22
χ2822222-2-2-22-2-2-2-2-22-2-2-2-222222-2-222000000000000000000000000000000000000-222-2
χ292222-222-2-2-222-2-2222-2-2-2-222-22-2-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ302222-222-2-2-222-2-2222-2-2-2-222-22-2-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ312222-222-2-2-222-2-22-2-222-2-22-22-222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ322222-222-2-2-222-2-22-2-222-2-22-22-222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ332222-222-2-2-2-2-222-2222222-22-2-2-22-2000000000000000000000000000000002i−2i2i−2i0000
χ342222-222-2-2-2-2-222-2222222-22-2-2-22-200000000000000000000000000000000−2i2i−2i2i0000
χ352222-222-2-2-2-2-222-2-2-2-2-222-2-2222-2200000000000000000000000000002i−2i2i−2i00000000
χ362222-222-2-2-2-2-222-2-2-2-2-222-2-2222-220000000000000000000000000000−2i2i−2i2i00000000
χ372222-2-2-22-2222-2-2-2222222-2-22-2-2-22000000000000000022-2-2-2-2220000000000000000
χ382222-2-2-22-2222-2-2-2222222-2-22-2-2-220000000000000000-2-22222-2-20000000000000000
χ392222-2-2-22-2222-2-2-2-2-2-2-222-22-2222-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402222-2-2-22-2222-2-2-2-2-2-2-222-22-2222-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412222-2-2-22-22-2-222222-2-2-2-22-222-22-200000000000000000000000000002i−2i−2i2i00000000
χ422222-2-2-22-22-2-222222-2-2-2-22-222-22-20000000000000000000000000000−2i2i2i−2i00000000
χ432222-2-2-22-22-2-2222-2-222-2-222-2-22-22000000000000000000000000000000002-2-220000
χ442222-2-2-22-22-2-2222-2-222-2-222-2-22-2200000000000000000000000000000000-222-20000
χ4522-2-222-22-2-22-22-2-200002-22000000i2−i2i2−i2i2−i2i2−i2002-2002-2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4622-2-222-22-2-22-22-2-200002-22000000i2−i2i2−i2i2−i2i2−i200-2200-22−i2i2−i2i2−i2i2−i2i20000000000000000
χ4722-2-222-22-2-22-22-2-200002-22000000−i2i2−i2i2−i2i2−i2i2002-2002-2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4822-2-222-22-2-22-22-2-200002-22000000−i2i2−i2i2−i2i2−i2i200-2200-22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4922-2-22-22-2-222-22-220000-22-2000000i2−i2i2−i2−i2i2−i2i2002i−2i00−2i2i−22−222−22−20000000000000000
χ5022-2-22-22-2-222-22-220000-22-2000000i2−i2i2−i2−i2i2−i2i200−2i2i002i−2i2−22−2−22−220000000000000000
χ5122-2-22-22-2-222-22-220000-22-2000000−i2i2−i2i2i2−i2i2−i2002i−2i00−2i2i2−22−2−22−220000000000000000
χ5222-2-22-22-2-222-22-220000-22-2000000−i2i2−i2i2i2−i2i2−i200−2i2i002i−2i−22−222−22−20000000000000000
χ5322-2-2-22-2-2222-2-22-20000-2220000002−2−222−2−222-2002-2002−2−222−2−220000000000000000
χ5422-2-2-22-2-2222-2-22-20000-2220000002−2−222−2−22-2200-2200−222−2−222−20000000000000000
χ5522-2-2-22-2-2222-2-22-20000-222000000−222−2−222−22-2002-200−222−2−222−20000000000000000
χ5622-2-2-22-2-2222-2-22-20000-222000000−222−2−222−2-2200-22002−2−222−2−220000000000000000
χ5722-2-2-2-2222-22-2-22200002-2-20000002−2−22−222−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ5822-2-2-2-2222-22-2-22200002-2-20000002−2−22−222−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ5922-2-2-2-2222-22-2-22200002-2-2000000−222−22−2−222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ6022-2-2-2-2222-22-2-22200002-2-2000000−222−22−2−22−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ6144-4-444-44-4-4-44-4440000-44-40000000000000000000000000000000000000000000000
χ6244-4-44-44-4-44-44-44-400004-440000000000000000000000000000000000000000000000
χ6344-4-4-44-4-444-444-4400004-4-40000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-444-4-40000-4440000000000000000000000000000000000000000000000
χ658-88-800000000000008-80000000000000000000000000000000000000000000000000
χ668-88-80000000000000-880000000000000000000000000000000000000000000000000
χ678-8-88000000000008-8000000000000000000000000000000000000000000000000000
χ688-8-8800000000000-88000000000000000000000000000000000000000000000000000

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