Finite Group Databasebeta

← Group #136921

Character table — Group #136921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884444444888844888888888161616161616161688888888881616161622
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111-1-1-1-11111-1-111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111-1-111-111-1-1-1-1-11-1-111-1-111-1-11-1ii−i−i111-1-1iiii−i−i−i−i11-1-1i−iii−i−iii−i−i1-1
χ101111-1-111-111-1-1-1-1-11-1-111-1-111-1-11-1ii−i−i111-1-1−i−i−i−iiiii-1-111i−iii−i−i−i−iii-11
χ111111-1-111-111-1-1-1-1-11-1-111-1-111-1-11-1−i−iii111-1-1iiii−i−i−i−i-1-111−ii−i−iiiii−i−i-11
χ121111-1-111-111-1-1-1-1-11-1-111-1-111-1-11-1−i−iii111-1-1−i−i−i−iiiii11-1-1−ii−i−iii−i−iii1-1
χ131111-1-111-111-1-1-1-1-11-1-1-1-11111-1-1-11ii−i−i1-1-111iiii−i−i−i−i11-1-1i−i−i−iii−i−iii-11
χ141111-1-111-111-1-1-1-1-11-1-1-1-11111-1-1-11ii−i−i1-1-111−i−i−i−iiiii-1-111i−i−i−iiiii−i−i1-1
χ151111-1-111-111-1-1-1-1-11-1-1-1-11111-1-1-11−i−iii1-1-111iiii−i−i−i−i-1-111−iiii−i−i−i−iii1-1
χ161111-1-111-111-1-1-1-1-11-1-1-1-11111-1-1-11−i−iii1-1-111−i−i−i−iiiii11-1-1−iiii−i−iii−i−i-11
χ17222222222222-2-2-2-22222222-2-2-2-2220000-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-20000-22222000000000000000000000000
χ192222222-2-2-22-20000-22-222-2-20000-22000000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ202222222-2-2-22-20000-22-222-2-20000-22000000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ212222222-2-2-22-20000-22-2-2-22200002-2000000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ222222222-2-2-22-20000-22-2-2-22200002-2000000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ23222222-2222-222222-2-2-2000022-2-2002222-20000000000000000-2-20000000000
χ24222222-2222-222222-2-2-2000022-2-200-2-2-2-2-20000000000000000220000000000
χ25222222-2222-22-2-2-2-2-2-2-20000-2-22200000020000000000000000002-22-2000000
χ26222222-2222-22-2-2-2-2-2-2-20000-2-2220000002000000000000000000-22-22000000
χ272222-2-222-222-222222-2-222-2-2-2-2222-20000-2-2-222000000000000000000000000
χ282222-2-222-222-222222-2-2-2-222-2-222-220000-222-2-2000000000000000000000000
χ292222-2-22-22-2220000-2-2222220000-2-200000000022−2−2−2−22200000000002−2−2200
χ302222-2-22-22-2220000-2-2222220000-2-2000000000−2−22222−2−20000000000−222−200
χ312222-2-22-22-2220000-2-22-2-2-2-200002200000000022−2−2−2−2220000000000−222−200
χ322222-2-22-22-2220000-2-22-2-2-2-2000022000000000−2−22222−2−200000000002−2−2200
χ332222-2-2-22-22-2-22222-2220000-2-2-2-200000020000000000000000002i−2i−2i2i000000
χ342222-2-2-22-22-2-22222-2220000-2-2-2-20000002000000000000000000−2i2i2i−2i000000
χ352222-2-2-22-22-2-2-2-2-2-2-22200002222002i2i−2i−2i-20000000000000000−2i2i0000000000
χ362222-2-2-22-22-2-2-2-2-2-2-2220000222200−2i−2i2i2i-200000000000000002i−2i0000000000
χ3722-2-22-2022-20-2-2-22200000002-200002-22-200000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-2-22-2022-20-2-2-22200000002-200002-22-200000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-2-22-2022-20-2-2-22200000002-20000-22-2200000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4022-2-22-2022-20-2-2-22200000002-20000-22-2200000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4122-2-2-2202-2-20222-2-200000002-200002i−2i−2i2i000002−22−2−22−22−i2i2i2−i2000000000000
χ4222-2-2-2202-2-20222-2-200000002-200002i−2i−2i2i00000−22−222−22−2i2−i2−i2i2000000000000
χ4322-2-2-2202-2-20222-2-200000002-20000−2i2i2i−2i000002−22−2−22−22i2−i2−i2i2000000000000
χ4422-2-2-2202-2-20222-2-200000002-20000−2i2i2i−2i00000−22−222−22−2−i2i2i2−i2000000000000
χ45444444-4-4-4-4-4-400004-440000000000000000000000000000000000000000000
χ464444-4-4-4-44-4-44000044-40000000000000000000000000000000000000000000
χ4744-4-44-4044-40-444-4-40000000-440000000000000000000000000000000000000
χ4844-4-44-40-4-4404000000000000000000000000002-2-222-2-220000000000000000
χ4944-4-44-40-4-440400000000000000000000000000-222-2-222-20000000000000000
χ5044-4-4-4404-4-404-4-4440000000-440000000000000000000000000000000000000
χ5144-4-4-440-4440-4000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5244-4-4-440-4440-400000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ534-44-4004000-4022−2222−22000004i−4i0022−2200000002i2−2i200000000000000000000000000
χ544-44-4004000-4022−2222−2200000−4i4i0022−220000000−2i22i200000000000000000000000000
χ554-44-4004000-40−2222−2222000004i−4i00−22220000000−2i22i200000000000000000000000000
χ564-44-4004000-40−2222−222200000−4i4i00−222200000002i2−2i200000000000000000000000000
χ574-44-400-40004022−2222−220004-40000−222200000000022−22000000000000000000000000
χ584-44-400-40004022−2222−22000-440000−2222000000000−2222000000000000000000000000
χ594-44-400-400040−2222−22220004-4000022−22000000000−2222000000000000000000000000
χ604-44-400-400040−2222−2222000-44000022−2200000000022−22000000000000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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