Finite Group Databasebeta

← Group #136374

Character table — Group #136374

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888822444444888161616161616161644888888881616161644
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111-1-1-1-1111111-1-1-1-11-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-1-1-1-111-1-1-1-1-11-1111ii−i−i1111-1-1ii−i−i-1i−i1111-1-1-1-11-1ii−i−i11-1-1ii−i−ii−i
χ101111-1-1-1-1-111-1-1-1-1-11-1111ii−i−i1111-1-1ii−i−i-1i−i-1-1-1-111111-1ii−i−i-1-111−i−iii−ii
χ111111-1-1-1-1-111-1-1-1-1-11-1111ii−i−i11-1-111ii−i−i-1i−i1111-1-1-1-1-11−i−iii-1-111ii−i−i−ii
χ121111-1-1-1-1-111-1-1-1-1-11-1111ii−i−i11-1-111ii−i−i-1i−i-1-1-1-11111-11−i−iii11-1-1−i−iiii−i
χ131111-1-1-1-1-111-1-1-1-1-11-1111−i−iii1111-1-1−i−iii-1−ii1111-1-1-1-11-1−i−iii11-1-1−i−iii−ii
χ141111-1-1-1-1-111-1-1-1-1-11-1111−i−iii1111-1-1−i−iii-1−ii-1-1-1-111111-1−i−iii-1-111ii−i−ii−i
χ151111-1-1-1-1-111-1-1-1-1-11-1111−i−iii11-1-111−i−iii-1−ii1111-1-1-1-1-11ii−i−i-1-111−i−iiii−i
χ161111-1-1-1-1-111-1-1-1-1-11-1111−i−iii11-1-111−i−iii-1−ii-1-1-1-11111-11ii−i−i11-1-1ii−i−i−ii
χ17222222222222-2-2-2-2222-2-22222-2-20000-2-2-2-2-222000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-200002222-2-2-2000000000000000000000000
χ192222222-2-22222222-2-2-2220000-2-222220000-20000000000-2-200000000000000
χ202222222-2-22222222-2-2-2220000-2-2-2-2-2-20000-200000000002200000000000000
χ212222222-2-2222-2-2-2-2-2-2-2-2-20000220000000020000000000002-22-20000000000
χ222222222-2-2222-2-2-2-2-2-2-2-2-2000022000000002000000000000-22-220000000000
χ23222222-2-2-2-2-2-2000022-2002i2i−2i−2i00000000000−2i2ii2i2−i2−i2i2i2−i2−i200000000002−22−200
χ24222222-2-2-2-2-2-2000022-2002i2i−2i−2i00000000000−2i2i−i2−i2i2i2−i2−i2i2i20000000000−22−2200
χ25222222-2-2-2-2-2-2000022-200−2i−2i2i2i000000000002i−2ii2i2−i2−i2i2i2−i2−i20000000000−22−2200
χ26222222-2-2-2-2-2-2000022-200−2i−2i2i2i000000000002i−2i−i2−i2i2i2−i2−i2i2i200000000002−22−200
χ272222-2-2222-2-2200002-2-200222200000000000-2-2i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i200
χ282222-2-2222-2-2200002-2-200222200000000000-2-2−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i200
χ292222-2-2222-2-2200002-2-200-2-2-2-20000000000022i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i200
χ302222-2-2222-2-2200002-2-200-2-2-2-20000000000022−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i200
χ312222-2-2-22222-22222-22-2-2-200002200000000-20000000000002i−2i−2i2i0000000000
χ322222-2-2-22222-22222-22-2-2-200002200000000-2000000000000−2i2i2i−2i0000000000
χ332222-2-2-22222-2-2-2-2-2-22-2220000-2-222-2-2000020000000000-2200000000000000
χ342222-2-2-22222-2-2-2-2-2-22-2220000-2-2-2-2220000200000000002-200000000000000
χ352222-2-2-2-2-222-222222-22-2-22i2i−2i−2i-2-20000−2i−2i2i2i22i−2i000000000000000000000000
χ362222-2-2-2-2-222-222222-22-2-2−2i−2i2i2i-2-200002i2i−2i−2i2−2i2i000000000000000000000000
χ3722-2-22-2-2002-2222-2-20002-20000002-22-20000000i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2000000
χ3822-2-22-2-2002-2222-2-20002-20000002-22-20000000−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2000000
χ3922-2-22-2-2002-2222-2-20002-2000000-22-220000000i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2000000
χ4022-2-22-2-2002-2222-2-20002-2000000-22-220000000−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2000000
χ4122-2-2-222002-2-2-2-2220002-20000002-2-220000000i2−i2i2−i2−i2i2−i2i2000000i2−i2−i2i2000000
χ4222-2-2-222002-2-2-2-2220002-20000002-2-220000000−i2i2−i2i2i2−i2i2−i2000000−i2i2i2−i2000000
χ4322-2-2-222002-2-2-2-2220002-2000000-222-20000000i2−i2i2−i2−i2i2−i2i2000000−i2i2i2−i2000000
χ4422-2-2-222002-2-2-2-2220002-2000000-222-20000000−i2i2−i2i2i2−i2i2−i2000000i2−i2−i2i2000000
χ45444444-444-4-4-40000-4-440000000000000000000000000000000000000000000
χ464444-4-44-4-4-4-440000-4440000000000000000000000000000000000000000000
χ4744-4-44-4400-44-4000000000000000000000000002-2-222-2-220000000000000000
χ4844-4-44-4400-44-400000000000000000000000000-222-2-222-20000000000000000
χ4944-4-44-4-4004-44-4-444000-4400000000000000000000000000000000000000000
χ5044-4-4-444004-4-444-4-4000-4400000000000000000000000000000000000000000
χ5144-4-4-44-400-444000000000000000000000000002-2-22-222-20000000000000000
χ5244-4-4-44-400-44400000000000000000000000000-222-22-2-220000000000000000
χ534-44-40004-40002i2−2i22i2−2i2000002i2−2i22i2−2i22i2−2i200002-22-2000000000000000000000000000
χ544-44-40004-40002i2−2i22i2−2i200000−2i22i2−2i22i22i2−2i20000-22-22000000000000000000000000000
χ554-44-40004-4000−2i22i2−2i22i2000002i2−2i22i2−2i2−2i22i20000-22-22000000000000000000000000000
χ564-44-40004-4000−2i22i2−2i22i200000−2i22i2−2i22i2−2i22i200002-22-2000000000000000000000000000
χ574-44-4000-440002i2−2i22i2−2i20000022−22−2222−2i22i200002i−2i−2i2i000000000000000000000000000
χ584-44-4000-440002i2−2i22i2−2i200000−222222−22−2i22i20000−2i2i2i−2i000000000000000000000000000
χ594-44-4000-44000−2i22i2−2i22i20000022−22−22222i2−2i20000−2i2i2i−2i000000000000000000000000000
χ604-44-4000-44000−2i22i2−2i22i200000−222222−222i2−2i200002i−2i−2i2i000000000000000000000000000
χ618-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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