Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C9⋊#6923 |
| unambiguous semidirect product | C9⋊(C7×#6923) |
| Fitting, Hall | C7×C9×C61 ⋊ C4 |
| derived, Hall | C9×C61 ⋊ C4×C7 |
| Hall | C7×C61 ⋊ Dic9 |
| Hall | C7×C9 ⋊ #6923 |
| Sylow | C61 ⋊ C7×Dic9 |
| Sylow | C9 ⋊ C7×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C9⋊#6923 |
| commutator, hypocenter | C9×C61 | C4×C7 |
| Frattini | C3 | C7×C3⋊#6923 |
| Fitting | C7×C9×C61 | C4 |
| socle | C3×C7×C61 | Dic3 |
| prime radical | C3×C7×D61 | D3 |
| cosocle | C9×D61 | C2×C7 |
| LCS | G ▷ C9×C61 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3843 |
1029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 53);