Finite Group DatabasebetaFinite Group Databasebeta| order | 5538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C13⋊C3)⋊D71 |
| unambiguous semidirect product | C71⋊(D13⋊C3) |
| unambiguous semidirect product | D923⋊C3 |
| Fitting, socle, derived, Hall | C13×C71 ⋊ C2×C3 |
| Hall | C13⋊C3×C71 ⋊ C2 |
| Hall | D923 ⋊ C3 |
| Sylow | C71 ⋊ D13⋊C3 |
| Hall | C13⋊C3 ⋊ D71 |
| Sylow | C13 ⋊ C3×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C71 | C2×C3 |
| LCS | G ▷ C13×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,71|c^a=c^12,d^a=d^70,c^b=c^3253 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5538, 12);