Finite Group Databasebeta

← Group #3711

Character table — Group #3711

Order 144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size11112222222244446666666666661818
order124433661212121236121224668812122424242488
χ1111111111111111111111111111111
χ211111111111111111111-1-111-1-1-1-1-1-1
χ31111111111111111-1-1-1-111-1-11111-1-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ511-1-11111-1-1-1-111-1-11-111i−i-1-1ii−i−ii−i
χ611-1-11111-1-1-1-111-1-11-111−ii-1-1−i−iii−ii
χ711-1-11111-1-1-1-111-1-1-11-1-1i−i11ii−i−i−ii
χ811-1-11111-1-1-1-111-1-1-11-1-1−ii11−i−iiii−i
χ922222-12-1-1-122-1-1-1-122-1-100-1-1000000
χ1022222-12-1-1-122-1-1-1-1-2-2110011000000
χ112222-12-1222-1-1-1-1-1-100002200-1-1-1-100
χ122222-12-1222-1-1-1-1-1-10000-2-200111100
χ1322-2-22-12-111-2-2-1-1112-2-1-10011000000
χ1422-2-22-12-111-2-2-1-111-221100-1-1000000
χ1522-2-2-12-12-2-211-1-11100002i−2i00−i−iii00
χ1622-2-2-12-12-2-211-1-1110000−2i2i00ii−i−i00
χ172-22i−2i22-2-22i−2i2i−2i2-22i−2i00000000000000
χ182-22i−2i2-1-21−ii2i−2i-11−ii00−i3i3003−3000000
χ192-22i−2i2-1-21−ii2i−2i-11−ii00i3−i300−33000000
χ202-22i−2i-121-22i−2i−ii-11−ii00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300
χ212-22i−2i-121-22i−2i−ii-11−ii00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300
χ222-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i00000000000000
χ232-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i300−33000000
χ242-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i3003−3000000
χ252-2−2i2i-121-2−2i2ii−i-11i−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300
χ262-2−2i2i-121-2−2i2ii−i-11i−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300
χ274444-2-2-2-2-2-2-2-2111100000000000000
χ2844-4-4-2-2-2-2222211-1-100000000000000
χ294-44i−4i-2-222−2i2i−2i2i1-1i−i00000000000000
χ304-4−4i4i-2-2222i−2i2i−2i1-1−ii00000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.