Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic13⋊C27 |
| derived, Sylow | C13 ⋊ C4×C27 |
| Hall | C13⋊C27 ⋊ C4 |
| Hall | Dic13 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C9 | D13⋊C3 |
| commutator, hypocenter | C13 | C4×C27 |
| Fitting, cosocle | C2×C9×C13 | C2×C3 |
| socle, prime radical | C2×C3×C13 | C2×C9 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C9 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1404 |
Polycyclic presentation:
2,3,2,3^2,13|a^2=c,b^3=d,d^3=e,f^a=f^12,f^b=f^9144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 1);