Finite Group Databasebeta

← Group #1480

Character table — Group #1480

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size11111111222222224444444444444444448888
order12224444224444444488888888888888882244
χ111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ611111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ711111111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-11-11
χ811111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1
χ91111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-1-11
χ101111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-111-1
χ111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-111-1
χ121111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-1-11
χ131111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iiiii−i−i−i−iii11-1-1
χ141111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iii−i−iiiii−i−i-1-111
χ151111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−iii−i−i−i−iii-1-111
χ161111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−i−i−iiiii−i−i11-1-1
χ172222222222-2-222-2-2-2-200000000000000000000
χ1822222222-2-2-2-2-2-2-2-22200000000000000000000
χ192222-2-2-2-222-2-2-2-222-2200000000000000000000
χ202222-2-2-2-2-2-2-2-222222-200000000000000000000
χ2122-2-22i−2i2i−2i002-2002i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ2222-2-22i−2i2i−2i002-2002i−2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ2322-2-22i−2i2i−2i00-2200−2i2i002ζ−2ζ2ζ3−2ζ30000000000000000
χ2422-2-22i−2i2i−2i00-2200−2i2i00−2ζ2ζ−2ζ32ζ30000000000000000
χ2522-2-2−2i2i−2i2i002-200−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ2622-2-2−2i2i−2i2i002-200−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ2722-2-2−2i2i−2i2i00-22002i−2i002ζ3−2ζ32ζ−2ζ0000000000000000
χ2822-2-2−2i2i−2i2i00-22002i−2i00−2ζ32ζ3−2ζ2ζ0000000000000000
χ292-2-2222-2-22-2002-2000000000000i2−i2i2−i2i2−i2i2−i20000
χ302-2-2222-2-22-2002-2000000000000−i2i2−i2i2−i2i2−i2i20000
χ312-2-2222-2-2-2200-22000000000000i2−i2i2−i2−i2i2−i2i20000
χ322-2-2222-2-2-2200-22000000000000−i2i2−i2i2i2−i2i2−i20000
χ332-2-22-2-2222-200-220000000000002−2−222−2−220000
χ342-2-22-2-2222-200-22000000000000−222−2−222−20000
χ352-2-22-2-222-22002-20000000000002−2−22−222−20000
χ362-2-22-2-222-22002-2000000000000−222−22−2−220000
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.