Finite Group Databasebeta

← Group #93613

Character table — Group #93613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order124422244444444488888888444488888888888816161616161616161616161616161616
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
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ141111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ151111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ161111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ17222222222222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-222-2-2000000000000000000000000
χ192222222222-2-2-2-2-2-222222222-2-222-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ2122222-2-22-2-22222-2-2220000-2-20000002-200000000i2−i2i2−i2i2−i2i2−i200000000
χ2222222-2-22-2-22222-2-2220000-2-20000002-200000000−i2i2−i2i2−i2i2−i2i200000000
χ2322222-2-22-2-22222-2-2-2-2000022000000-22000000002−22−2−22−2200000000
χ2422222-2-22-2-22222-2-2-2-2000022000000-2200000000−22−222−22−200000000
χ2522222-2-22-2-2-2-2-2-222220000-2-2000000-22000000002−2−222−2−2200000000
χ2622222-2-22-2-2-2-2-2-222220000-2-2000000-2200000000−222−2−222−200000000
χ2722222-2-22-2-2-2-2-2-222-2-20000220000002-200000000i2−i2−i2i2−i2i2i2−i200000000
χ2822222-2-22-2-2-2-2-2-222-2-20000220000002-200000000−i2i2i2−i2i2−i2−i2i200000000
χ2922-2-22-2-2-2220000002i−2i22-2-22i−2i002i−2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ3022-2-22-2-2-2220000002i−2i22-2-22i−2i002i−2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ3122-2-22-2-2-2220000002i−2i-2-2222i−2i00−2i2i00001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ3222-2-22-2-2-2220000002i−2i-2-2222i−2i00−2i2i0000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ3322-2-22-2-2-222000000−2i2i22-2-2−2i2i00−2i2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ3422-2-22-2-2-222000000−2i2i22-2-2−2i2i00−2i2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ3522-2-22-2-2-222000000−2i2i-2-222−2i2i002i−2i00001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ3622-2-22-2-2-222000000−2i2i-2-222−2i2i002i−2i0000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ3722-2-2-22-222-22i2i−2i−2i2i−2i002i−2i2i−2i0000002-20000000000000000002−2i2−i22−2i2−i2
χ3822-2-2-22-222-22i2i−2i−2i2i−2i002i−2i2i−2i0000002-2000000000000000000−22−i2i2−22−i2i2
χ3922-2-2-22-222-22i2i−2i−2i2i−2i00−2i2i−2i2i000000-22000000000000000000i2−i2−22−i2i22−2
χ4022-2-2-22-222-22i2i−2i−2i2i−2i00−2i2i−2i2i000000-22000000000000000000−i2i22−2i2−i2−22
χ4122-2-2-22-222-2−2i−2i2i2i−2i2i002i−2i2i−2i000000-22000000000000000000i2−i22−2−i2i2−22
χ4222-2-2-22-222-2−2i−2i2i2i−2i2i002i−2i2i−2i000000-22000000000000000000−i2i2−22i2−i22−2
χ4322-2-2-22-222-2−2i−2i2i2i−2i2i00−2i2i−2i2i0000002-20000000000000000002−2−i2i22−2−i2i2
χ4422-2-2-22-222-2−2i−2i2i2i−2i2i00−2i2i−2i2i0000002-2000000000000000000−22i2−i2−22i2−i2
χ454444-44-4-4-44000000000000004i−4i000000000000000000000000000000
χ464444-44-4-4-4400000000000000−4i4i000000000000000000000000000000
χ474444-4-44-44-4000000004i−4i−4i4i0000000000000000000000000000000000
χ484444-4-44-44-400000000−4i4i4i−4i0000000000000000000000000000000000
χ4944-4-4444-4-4-40000004i−4i0000−4i4i00000000000000000000000000000000
χ5044-4-4444-4-4-4000000−4i4i00004i−4i00000000000000000000000000000000
χ5144-4-4-4-444-444i4i−4i−4i−4i4i0000000000000000000000000000000000000000
χ5244-4-4-4-444-44−4i−4i4i4i4i−4i0000000000000000000000000000000000000000
χ538-88i−8i0000004+4i−4−4i4−4i−4+4i000000000000000000000000000000000000000000
χ548-88i−8i000000−4−4i4+4i−4+4i4−4i000000000000000000000000000000000000000000
χ558-8−8i8i0000004−4i−4+4i4+4i−4−4i000000000000000000000000000000000000000000
χ568-8−8i8i000000−4+4i4−4i−4−4i4+4i000000000000000000000000000000000000000000

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