Finite Group DatabasebetaFinite Group Databasebeta| order | 1872 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D13⋊SL(2,𝔽3)) |
| unambiguous semidirect product | D39⋊SL(2,𝔽3) |
| Fitting, derived | C3×Q8×C13 ⋊ C2×C3 |
| Sylow | C13 ⋊ D3×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D13⋊A4) |
| commutator, Fitting, cosocle, hypocenter | C3×Q8×C13 | C2×C3 |
| socle | C2×C3×C13 | C2×A4 |
| LCS | G ▷ C3×Q8×C13 | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2,3,2^2,3,13,2|c^2=g,d^2=g,e^a=e^2,f^a=f^12,c^b=d,d^b=cd,f^b=f^3,d^c=dg51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1872, 780);