Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×D13⋊C27 |
| unambiguous semidirect product | D13⋊(C2×C27) |
| unambiguous semidirect product | (C2×D13)⋊C27 |
| unambiguous semidirect product | (C13⋊C27)⋊C22 |
| unambiguous semidirect product | (C2×C13⋊C27)⋊C2 |
| derived, Sylow | C13 ⋊ C22×C27 |
| Hall | C13⋊C27 ⋊ C22 |
| Hall | C2×D13 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D13⋊C3 |
| commutator, hypocenter | C13 | C22×C27 |
| Frattini | C9 | C2×D13⋊C3 |
| Fitting | C2×C9×C13 | C2×C3 |
| socle | C2×C3×C13 | C2×C9 |
| prime radical | C2×C3×D13 | C9 |
| cosocle | C9×C13 | C22×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C9 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 702 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 8);