Finite Group Databasebeta

← Group #135307

Character table — Group #135307

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444422444444444444448888888888888888
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
χ51111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-222-2-2-2-22222000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000
χ2122-2-22-2-2222-2-222-2-2002i2i−2i−2i000000002i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ2222-2-22-2-2222-2-222-2-2002i2i−2i−2i000000002i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ2322-2-22-2-2222-2-222-2-200−2i−2i2i2i00000000−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ2422-2-22-2-2222-2-222-2-200−2i−2i2i2i00000000−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ2522-2-22-2-2222-2-2-2-222002i2i−2i−2i00000000−2i2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ2622-2-22-2-2222-2-2-2-222002i2i−2i−2i00000000−2i2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ2722-2-22-2-2222-2-2-2-22200−2i−2i2i2i000000002i−2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ2822-2-22-2-2222-2-2-2-22200−2i−2i2i2i000000002i−2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ2922-2-22-2-22-2-2222-22-2220000-2-22-200000000000000i2−i2i2−i2i2−i2i2−i200000000
χ3022-2-22-2-22-2-2222-22-2220000-2-22-200000000000000−i2i2−i2i2−i2i2−i2i200000000
χ3122-2-22-2-22-2-2222-22-2-2-2000022-22000000000000002−22−2−22−2200000000
χ3222-2-22-2-22-2-2222-22-2-2-2000022-2200000000000000−22−222−22−200000000
χ3322-2-22-2-22-2-222-22-22220000-2-2-2200000000000000i2−i2−i2i2i2−i2−i2i200000000
χ3422-2-22-2-22-2-222-22-22220000-2-2-2200000000000000−i2i2i2−i2−i2i2i2−i200000000
χ3522-2-22-2-22-2-222-22-22-2-20000222-2000000000000002−2−22−222−200000000
χ3622-2-22-2-22-2-222-22-22-2-20000222-200000000000000−222−22−2−2200000000
χ372-2-2-2222-22-22-200002-22-22-22-2002-20000002i−2i002i−2i0000000000000000
χ382-2-2-2222-22-22-200002-22-22-22-2002-2000000−2i2i00−2i2i0000000000000000
χ392-2-2-2222-22-22-200002-2-22-222-200-2200002i−2i002i−2i000000000000000000
χ402-2-2-2222-22-22-200002-2-22-222-200-220000−2i2i00−2i2i000000000000000000
χ412-2-2-2222-22-22-20000-222-22-2-2200-2200002i−2i00−2i2i000000000000000000
χ422-2-2-2222-22-22-20000-222-22-2-2200-220000−2i2i002i−2i000000000000000000
χ432-2-2-2222-22-22-20000-22-22-22-22002-20000002i−2i00−2i2i0000000000000000
χ442-2-2-2222-22-22-20000-22-22-22-22002-2000000−2i2i002i−2i0000000000000000
χ4544444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ4644444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ474-4444-4-4-44-4-440000004i−4i−4i4i0000000000000000000000000000000000
χ484-4444-4-4-44-4-44000000−4i4i4i−4i0000000000000000000000000000000000
χ494-4444-4-4-4-444-400004-40000-4400000000000000000000000000000000
χ504-4444-4-4-4-444-40000-4400004-400000000000000000000000000000000
χ514-4-4-4444-4-44-4400000000000000004-400000000000000000000000000
χ524-4-4-4444-4-44-440000000000000000-4400000000000000000000000000
χ53888-8-88-8-8000000000000000000000000000000000000000000000000
χ5488-88-8-88-8000000000000000000000000000000000000000000000000
χ558-88-8-8-888000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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