Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic13⋊C9 |
| unambiguous semidirect product | (C3×Dic13)⋊C9 |
| derived, Sylow | C13 ⋊ C3×C4×C9 |
| Hall | C3×C13⋊C9 ⋊ C4 |
| Hall | Dic13 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D13⋊C3 |
| commutator, hypocenter | C13 | C3×C4×C9 |
| Frattini | C2×C3 | C3×D13⋊C3 |
| Fitting, socle, prime radical | C2×C32×C13 | C2×C3 |
| cosocle | C2×C3×C13 | C2×C32 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1404 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 22);