Finite Group Databasebeta

← Group #65740

Character table — Group #65740

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35
size1122244445555558881010101010101010101616202020202020
order12488445104488882040402444488882020228888
χ111111111111111111111111111111111111
χ211111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ3111111111-1-1ii−i−i111-1ii−i−i-1-1i−i11-1-1ii−i−i
χ4111111111-1-1−i−iii111-1−i−iii-1-1−ii11-1-1−i−iii
χ511111-1-111111111111111111111-1-1-1-1-1-1-1-1
χ611111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111
χ711111-1-111-1-1ii−i−i111-1ii−i−i-1-1i−i-1-111−i−iii
χ811111-1-111-1-1−i−iii111-1−i−iii-1-1−ii-1-111ii−i−i
χ9111-1-11-1111111111-1-11-1-1-1-1-1-1111-11-11-11-1
χ10111-1-11-11111-1-1-1-11-1-111111-1-1-1-11-11-1-11-11
χ11111-1-11-111-1-1ii−i−i1-1-1-1−i−iii11i−i1-1-11i−i−ii
χ12111-1-11-111-1-1−i−iii1-1-1-1ii−i−i11−ii1-1-11−iii−i
χ13111-1-1-11111111111-1-11-1-1-1-1-1-111-11-11-11-11
χ14111-1-1-111111-1-1-1-11-1-111111-1-1-1-1-11-111-11-1
χ15111-1-1-1111-1-1ii−i−i1-1-1-1−i−iii11i−i-111-1−iii−i
χ16111-1-1-1111-1-1−i−iii1-1-1-1ii−i−i11−ii-111-1i−i−ii
χ1722-2000022222222-200-2000000-2-200000000
χ1822-200002222-2-2-2-2-200-20000002200000000
χ1922-2000022-2-22i2i−2i−2i-2002000000−2i2i00000000
χ2022-2000022-2-2−2i−2i2i2i-20020000002i−2i00000000
χ212-202−2002-22i−2i2ζ−2ζ2ζ3−2ζ302−201+i−1−i1−i−1+ii2−i20000000000
χ222-202−2002-22i−2i−2ζ2ζ−2ζ32ζ302−20−1−i1+i−1+i1−ii2−i20000000000
χ232-202−2002-2−2i2i2ζ3−2ζ32ζ−2ζ02−20−1+i1−i−1−i1+i−i2i20000000000
χ242-202−2002-2−2i2i−2ζ32ζ3−2ζ2ζ02−201−i−1+i1+i−1−i−i2i20000000000
χ252-20−22002-22i−2i2ζ−2ζ2ζ3−2ζ30−220−1−i1+i−1+i1−i−i2i20000000000
χ262-20−22002-22i−2i−2ζ2ζ−2ζ32ζ30−2201+i−1−i1−i−1+i−i2i20000000000
χ272-20−22002-2−2i2i2ζ3−2ζ32ζ−2ζ0−2201−i−1+i1+i−1−ii2−i20000000000
χ282-20−22002-2−2i2i−2ζ32ζ3−2ζ2ζ0−220−1+i1−i−1−i1+ii2−i20000000000
χ294444444-1-1000000-1-1-1000000000-1-1000000
χ3044444-4-4-1-1000000-1-1-100000000011000000
χ31444-4-44-4-1-1000000-111000000000-11000000
χ32444-4-4-44-1-1000000-1110000000001-1000000
χ3388-80000-2-200000020000000000000000000
χ348-8042−4200-220000000−2200000000000000000
χ358-80−424200-2200000002−200000000000000000

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