Finite Group DatabasebetaFinite Group Databasebeta| order | 16172 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic311 |
| unambiguous semidirect product | C311⋊(C4×C13) |
| derived, Sylow | C311 ⋊ C4×C13 |
| Hall | C13×C311 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D311 |
| commutator, hypocenter | C311 | C4×C13 |
| Frattini | C2 | C13×D311 |
| Fitting, socle, prime radical | C2×C13×C311 | C2 |
| cosocle | C2×C311 | C2×C13 |
| LCS | G ▷ C311 | |
| UCS | C1 ◁ C2×C13 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16172 |
4082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16172, 3);