Finite Group Databasebeta

← Group #93191

Character table — Group #93191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222248888888888881616161616161616161616161616161616161616163232
order12222222222444444444422444888888888888888888
χ111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111-1-1-1-11-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ6111111111111-1-1-1-11-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ7111111111111-1-1-1-11-1-1-1-11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ8111111111111-1-1-1-11-1-1-1-11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-11111ii−i−i-1ii−i−i-11-1-11ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3i−i
χ101111-1-1-1-11111ii−i−i-1ii−i−i-11-1-11−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3i−i
χ111111-1-1-1-11111ii−i−i-1ii−i−i-1-111-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ii
χ121111-1-1-1-11111ii−i−i-1ii−i−i-1-111-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ii
χ131111-1-1-1-11111−i−iii-1−i−iii-11-1-11ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ii
χ141111-1-1-1-11111−i−iii-1−i−iii-11-1-11−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ii
χ151111-1-1-1-11111−i−iii-1−i−iii-1-111-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζi−i
χ161111-1-1-1-11111−i−iii-1−i−iii-1-111-1−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζi−i
χ17222222222-2-222-22-222-22-2-20000000000000000000000
χ18222222222-2-22-22-222-22-22-20000000000000000000000
χ192222-2-2-2-22-2-222i−2i−2i2i-22i−2i−2i2i20000000000000000000000
χ202222-2-2-2-22-2-22−2i2i2i−2i-2−2i2i2i−2i20000000000000000000000
χ2144444444400-40000-4000000000000000000000000000
χ2244444-44-4-4000000000000022-2-2000000000000000000
χ2344444-44-4-40000000000000-2-222000000000000000000
χ244444-44-44-400000000000002-22-2000000000000000000
χ254444-44-44-40000000000000-22-22000000000000000000
χ264444-4-4-4-4400-400004000000000000000000000000000
χ2744-4-4040-400002i0−2i00−2i02i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ2844-4-4040-400002i0−2i00−2i02i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ2944-4-4040-40000−2i02i002i0−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ3044-4-4040-40000−2i02i002i0−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ3144-4-40-404000020200-20-2000000i2−i2−i2i2i2−i2−i2i20000000000
χ3244-4-40-404000020200-20-2000000−i2i2i2−i2−i2i2i2−i20000000000
χ3344-4-40-4040000-20-2002020000002−2−22−222−20000000000
χ3444-4-40-4040000-20-200202000000−222−22−2−220000000000
χ354-44-440-40000002i0−2i00−2i02i00000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00
χ364-44-440-40000002i0−2i00−2i02i0000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00
χ374-44-440-4000000−2i02i002i0−2i00000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00
χ384-44-440-4000000−2i02i002i0−2i0000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00
χ394-44-4-40400000020200-20-20000000000000i2−i2−i2i2i2−i2−i2i200
χ404-44-4-40400000020200-20-20000000000000−i2i2i2−i2−i2i2i2−i200
χ414-44-4-404000000-20-20020200000000000002−2−22−222−200
χ424-44-4-404000000-20-2002020000000000000−222−22−2−2200
χ438-8-88000004-4000000000000000000000000000000000
χ448-8-8800000-44000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.