Finite Group Databasebeta

← Group #9788

Character table — Group #9788

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order1222224444444488888888448888888888888888888844448888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911111111-1-1-1-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ1011111111-1-1-1-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ1111111111-1-1-1-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ1211111111-1-1-1-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ1311111111-1-1-1-1-1-1-1-1-1-111111-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ1411111111-1-1-1-1-1-1-1-1-1-111111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ1511111111-1-1-1-1-1-1-1-1-1-111111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ1611111111-1-1-1-1-1-1-1-1-1-111111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ17222222-2-222-2-22200000000-2-200000000000022-2-222-2-200000000
χ18222222-2-222-2-22200000000-2-2000000000000-2-222-2-22200000000
χ19222222-2-2-2-222-2-200000000-220000000000002i2i−2i−2i−2i−2i2i2i00000000
χ20222222-2-2-2-222-2-200000000-22000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ212222-2-2222222-2-222222222-2-2-2-2-2-2000000000000000000000000
χ222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ232222-2-222-2-2-2-2222222-2-2-2-2-22-2-222000000000000000000000000
χ242222-2-222-2-2-2-222-2-2-2-22222-2222-2-2000000000000000000000000
χ252222-2-2-2-222-2-2-2-2000000002200002i2i−2i−2i2i2i−2i−2i0000000000000000
χ262222-2-2-2-222-2-2-2-200000000220000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ272222-2-2-2-2-2-22222000000002-2000022-2-2-2-2220000000000000000
χ282222-2-2-2-2-2-22222000000002-20000-2-22222-2-20000000000000000
χ292-22-22-2002i−2i002i−2ii2i2−i2−i222−2−200i2−i22−21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ00000000
χ302-22-22-2002i−2i002i−2ii2i2−i2−i222−2−200i2−i22−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ00000000
χ312-22-22-2002i−2i002i−2i−i2−i2i2i2−2−22200−i2i2−221+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ00000000
χ322-22-22-2002i−2i002i−2i−i2−i2i2i2−2−22200−i2i2−22−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ00000000
χ332-22-22-200−2i2i00−2i2ii2i2−i2−i2−2−22200i2−i2−221−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ300000000
χ342-22-22-200−2i2i00−2i2ii2i2−i2−i2−2−22200i2−i2−22−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ300000000
χ352-22-22-200−2i2i00−2i2i−i2−i2i2i222−2−200−i2i22−21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ300000000
χ362-22-22-200−2i2i00−2i2i−i2−i2i2i222−2−200−i2i22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ300000000
χ372-22-2-22002i−2i00−2i2ii2i2−i2−i222−2−200−i2i2−221−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ30000000000
χ382-22-2-22002i−2i00−2i2ii2i2−i2−i222−2−200−i2i2−22−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ30000000000
χ392-22-2-22002i−2i00−2i2i−i2−i2i2i2−2−22200i2−i22−21−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ30000000000
χ402-22-2-22002i−2i00−2i2i−i2−i2i2i2−2−22200i2−i22−2−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ30000000000
χ412-22-2-2200−2i2i002i−2ii2i2−i2−i2−2−22200−i2i22−21+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ0000000000
χ422-22-2-2200−2i2i002i−2ii2i2−i2−i2−2−22200−i2i22−2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ0000000000
χ432-22-2-2200−2i2i002i−2i−i2−i2i2i222−2−200i2−i2−221+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ0000000000
χ442-22-2-2200−2i2i002i−2i−i2−i2i2i222−2−200i2−i2−22−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ0000000000
χ4544-4-4004-400000000004-44-4000000000000000000000000000000
χ4644-4-4004-40000000000-44-44000000000000000000000000000000
χ4744-4-400-440000004-44-40000000000000000000000000000000000
χ4844-4-400-44000000-44-440000000000000000000000000000000000
χ494-4-440000004i−4i002i2−2i2−2i22i222−22−2222000000000000000000000000000000
χ504-4-440000004i−4i00−2i22i22i2−2i2−222222−22000000000000000000000000000000
χ514-4-44000000−4i4i002i2−2i2−2i22i2−222222−22000000000000000000000000000000
χ524-4-44000000−4i4i00−2i22i22i2−2i222−22−2222000000000000000000000000000000

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