Finite Group DatabasebetaFinite Group Databasebeta| order | 21372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic411 |
| unambiguous semidirect product | C3⋊(C13×Dic137) |
| derived, Hall | C3×C137 ⋊ C4×C13 |
| Hall | C3×C13×C137 ⋊ C4 |
| Hall | C13×C137 ⋊ Dic3 |
| Sylow | C137 ⋊ Dic3×C13 |
| Hall | C3×C13 ⋊ Dic137 |
| Sylow | C3 ⋊ C13×Dic137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D411 |
| commutator, hypocenter | C3×C137 | C4×C13 |
| Frattini | C2 | C13×D411 |
| Fitting, socle, prime radical | C2×C3×C13×C137 | C2 |
| cosocle | C2×C3×C137 | C2×C13 |
| LCS | G ▷ C3×C137 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21372 |
5382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21372, 7);