Finite Group Databasebeta

← Group #141997

Character table — Group #141997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444488882244444488888844888816161616161616161616161616161616444444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ121111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2220000000000000000000000000000
χ1822222222222222-2-2-2-22222222222-2-2-2-2-2-20000000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2220000000000000000000000000000
χ21222222-2-2-2-2000022-2-222-2-2000000-22000022−2−222−2−222−2−222−2−2000000000000
χ22222222-2-2-2-2000022-2-222-2-2000000-220000−2−222−2−222−2−222−2−222000000000000
χ23222222-2-2-2-2000022-2-2-2-2220000002-2000022−2−2−2−22222−2−2−2−222000000000000
χ24222222-2-2-2-2000022-2-2-2-2220000002-20000−2−22222−2−2−2−22222−2−2000000000000
χ25222222-2-2-2-20000-2-22222-2-20000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ26222222-2-2-2-20000-2-22222-2-20000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ27222222-2-2-2-20000-2-222-2-222000000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ28222222-2-2-2-20000-2-222-2-222000000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2922-2-22-22-22-200002-22-200000022-2-2002-20000002-22-200002-22-2000000000000
χ3022-2-22-22-22-200002-22-200000022-2-2002-2000000-22-220000-22-22000000000000
χ3122-2-22-22-22-200002-22-2000000-2-22200-22002-22-200002-22-20000000000000000
χ3222-2-22-22-22-200002-22-2000000-2-22200-2200-22-220000-22-220000000000000000
χ3322-2-22-22-22-20000-22-2200000022-2-200-22002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ3422-2-22-22-22-20000-22-2200000022-2-200-2200−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ3522-2-22-22-22-20000-22-22000000-2-222002-20000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ3622-2-22-22-22-20000-22-22000000-2-222002-2000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ3722-2-22-2-22-2222-2-22-2-2200002-2000000002-22−2−222−2−222−2−222−2−22000000000000
χ3822-2-22-2-22-2222-2-22-2-2200002-2000000002-2−222−2−222−2−222−2−222−2000000000000
χ3922-2-22-2-22-2222-2-2-222-200002-200000000-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ4022-2-22-2-22-2222-2-2-222-200002-200000000-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ4122-2-22-2-22-22-2-2222-2-220000-2200000000-222−2−22−222−22−2−22−222−2000000000000
χ4222-2-22-2-22-22-2-2222-2-220000-2200000000-22−222−22−2−22−222−22−2−22000000000000
χ4322-2-22-2-22-22-2-222-222-20000-22000000002-2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ4422-2-22-2-22-22-2-222-222-20000-22000000002-2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ4522-2-2-222-2-2222-2-200002i−2i2i−2i-222i−2i2i−2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ4622-2-2-222-2-2222-2-200002i−2i2i−2i-222i−2i2i−2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ4722-2-2-222-2-2222-2-20000−2i2i−2i2i-22−2i2i−2i2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ4822-2-2-222-2-2222-2-20000−2i2i−2i2i-22−2i2i−2i2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ4922-2-2-222-2-22-2-22200002i−2i2i−2i2-2−2i2i−2i2i00000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ5022-2-2-222-2-22-2-22200002i−2i2i−2i2-2−2i2i−2i2i0000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ5122-2-2-222-2-22-2-2220000−2i2i−2i2i2-22i−2i2i−2i00000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ5222-2-2-222-2-22-2-2220000−2i2i−2i2i2-22i−2i2i−2i0000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ534444-4-444-4-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ544444-4-444-4-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ554444-4-4-4-444444400000000-4-400000000000000000000000000000000000000
χ564444-4-4-4-444-4-4-4-4000000004400000000000000000000000000000000000000
χ5744-4-4-44-444-4000000004i−4i−4i4i0000000000000000000000000000000000000000
χ5844-4-4-44-444-400000000−4i4i4i−4i0000000000000000000000000000000000000000
χ598-88-800000042−4242−42000000000000000000000000000000000000000000000000
χ608-88-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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