Finite Group Databasebeta

← Group #1876

Character table — Group #1876

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size11111111222222224444444444444444448888
order12224444224488882244444488888888882488
χ111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ41111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ6111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1
χ8111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ91111-1-1-1-1-1-111ii−i−i11-1-1ii−i−ii−iii−i−i11-1-11-1i−i
χ101111-1-1-1-1-1-111ii−i−i11-1-1−i−iiii−iii−i−i-1-111-11−ii
χ111111-1-1-1-1-1-111ii−i−i-1-111ii−i−ii−i−i−iii11-1-1-11−ii
χ121111-1-1-1-1-1-111ii−i−i-1-111−i−iiii−i−i−iii-1-1111-1i−i
χ131111-1-1-1-1-1-111−i−iii11-1-1ii−i−i−ii−i−iii-1-111-11i−i
χ141111-1-1-1-1-1-111−i−iii11-1-1−i−iii−ii−i−iii11-1-11-1−ii
χ151111-1-1-1-1-1-111−i−iii-1-111ii−i−i−iiii−i−i-1-1111-1−ii
χ161111-1-1-1-1-1-111−i−iii-1-111−i−iii−iiii−i−i11-1-1-11i−i
χ1722222222-2-2-2-2222200000000-2-2000000000000
χ1822222222-2-2-2-2-2-2-2-20000000022000000000000
χ192222-2-2-2-222-2-22i2i−2i−2i00000000−2i2i000000000000
χ202222-2-2-2-222-2-2−2i−2i2i2i000000002i−2i000000000000
χ2122-2-22i−2i2i−2i00002ζ−2ζ2ζ3−2ζ300001+i−1−i1−i−1+i0000002−2i2−i20000
χ2222-2-22i−2i2i−2i00002ζ−2ζ2ζ3−2ζ30000−1−i1+i−1+i1−i000000−22−i2i20000
χ2322-2-22i−2i2i−2i0000−2ζ2ζ−2ζ32ζ300001+i−1−i1−i−1+i000000−22−i2i20000
χ2422-2-22i−2i2i−2i0000−2ζ2ζ−2ζ32ζ30000−1−i1+i−1+i1−i0000002−2i2−i20000
χ2522-2-2−2i2i−2i2i00002ζ3−2ζ32ζ−2ζ00001−i−1+i1+i−1−i000000−22i2−i20000
χ2622-2-2−2i2i−2i2i00002ζ3−2ζ32ζ−2ζ0000−1+i1−i−1−i1+i0000002−2−i2i20000
χ2722-2-2−2i2i−2i2i0000−2ζ32ζ3−2ζ2ζ00001−i−1+i1+i−1−i0000002−2−i2i20000
χ2822-2-2−2i2i−2i2i0000−2ζ32ζ3−2ζ2ζ0000−1+i1−i−1−i1+i000000−22i2−i20000
χ292-2-2222-2-22-22-2000000000000002i−2i2i−2i00000000
χ302-2-2222-2-22-22-200000000000000−2i2i−2i2i00000000
χ312-2-2222-2-2-22-2200002-22-2000000000000000000
χ322-2-2222-2-2-22-220000-22-22000000000000000000
χ332-2-22-2-2222-2-2200002-2-22000000000000000000
χ342-2-22-2-2222-2-220000-222-2000000000000000000
χ352-2-22-2-222-222-2000000000000002-2-2200000000
χ362-2-22-2-222-222-200000000000000-222-200000000
χ374-44-44i−4i−4i4i000000000000000000000000000000
χ384-44-4−4i4i4i−4i000000000000000000000000000000

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