Finite Group Databasebeta

← Group #135402

Character table — Group #135402

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order124422244444444488888888244488888888888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111-1-1-1-1111-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1
χ101111111-1-1-1-1111-1-111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-111
χ111111111-1-1-1-1111-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111
χ121111111-1-1-1-1111-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1
χ131111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-2-2-222000000000000000000000000
χ192222222-2-2-2-2222-2-22222-2-2-2-222-2-2-2-222000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-2222222-2-222-2-2000000000000000000000000
χ2122-2-22-2-22i2i−2i−2i2-222i−2i00002i2i−2i−2i0000002-2000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ2222-2-22-2-22i2i−2i−2i2-222i−2i00002i2i−2i−2i0000002-200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ2322-2-22-2-22i2i−2i−2i2-222i−2i0000−2i−2i2i2i000000-22000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ2422-2-22-2-22i2i−2i−2i2-222i−2i0000−2i−2i2i2i000000-2200000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ2522-2-22-2-2−2i−2i2i2i2-22−2i2i00002i2i−2i−2i000000-22000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ2622-2-22-2-2−2i−2i2i2i2-22−2i2i00002i2i−2i−2i000000-2200000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ2722-2-22-2-2−2i−2i2i2i2-22−2i2i0000−2i−2i2i2i0000002-2000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ2822-2-22-2-2−2i−2i2i2i2-22−2i2i0000−2i−2i2i2i0000002-200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ2922-2-2-22-22i2i−2i−2i-222−2i2i2i2i−2i−2i000000002-20000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ3022-2-2-22-22i2i−2i−2i-222−2i2i2i2i−2i−2i000000002-2000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ3122-2-2-22-22i2i−2i−2i-222−2i2i−2i−2i2i2i00000000-220000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ3222-2-2-22-22i2i−2i−2i-222−2i2i−2i−2i2i2i00000000-22000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ3322-2-2-22-2−2i−2i2i2i-2222i−2i2i2i−2i−2i00000000-220000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ3422-2-2-22-2−2i−2i2i2i-2222i−2i2i2i−2i−2i00000000-22000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ3522-2-2-22-2−2i−2i2i2i-2222i−2i−2i−2i2i2i000000002-20000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ3622-2-2-22-2−2i−2i2i2i-2222i−2i−2i−2i2i2i000000002-2000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ3722-2-2-2-22000022-2002-22-22-22-2002-20000002i−2i2i−2i000000000000000000
χ3822-2-2-2-22000022-2002-22-22-22-2002-2000000−2i2i−2i2i000000000000000000
χ3922-2-2-2-22000022-2002-22-2-22-2200-2200002i−2i00002i−2i0000000000000000
χ4022-2-2-2-22000022-2002-22-2-22-2200-220000−2i2i0000−2i2i0000000000000000
χ4122-2-2-2-22000022-200-22-222-22-200-2200002i−2i0000−2i2i0000000000000000
χ4222-2-2-2-22000022-200-22-222-22-200-220000−2i2i00002i−2i0000000000000000
χ4322-2-2-2-22000022-200-22-22-22-22002-20000002i−2i−2i2i000000000000000000
χ4422-2-2-2-22000022-200-22-22-22-22002-2000000−2i2i2i−2i000000000000000000
χ4544444-4-40000-44-4004i−4i−4i4i000000000000000000000000000000000000
χ4644444-4-40000-44-400−4i4i4i−4i000000000000000000000000000000000000
χ474444-44-400004-4-40000004i−4i−4i4i00000000000000000000000000000000
χ484444-44-400004-4-4000000−4i4i4i−4i00000000000000000000000000000000
χ494444-4-444444-4-44-4-40000000000000000000000000000000000000000
χ504444-4-44-4-4-4-4-4-44440000000000000000000000000000000000000000
χ5144-4-44440000-4-4-400000000004-4000000000000000000000000000000
χ5244-4-44440000-4-4-40000000000-44000000000000000000000000000000
χ538-88i−8i0004+4i−4−4i4−4i−4+4i000000000000000000000000000000000000000000000
χ548-88i−8i000−4−4i4+4i−4+4i4−4i000000000000000000000000000000000000000000000
χ558-8−8i8i0004−4i−4+4i4+4i−4−4i000000000000000000000000000000000000000000000
χ568-8−8i8i000−4+4i4−4i−4−4i4+4i000000000000000000000000000000000000000000000

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