Finite Group DatabasebetaFinite Group Databasebeta| order | 36372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊#13181884 |
| unambiguous semidirect product | C3⋊(C7×#13181884) |
| Fitting, socle, Hall | C3×C7×C433 ⋊ C4 |
| derived, Hall | C3×C433 ⋊ C4×C7 |
| Hall | C7×C433 ⋊ Dic3 |
| Sylow | C433 ⋊ C7×Dic3 |
| Hall | C3×C7 ⋊ #13181884 |
| Sylow | C3 ⋊ C7×#13181884 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊#13181884 |
| commutator, hypocenter | C3×C433 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C433 | C4 |
| prime radical | C3×C7×D433 | C2 |
| cosocle | C3×D433 | C2×C7 |
| LCS | G ▷ C3×C433 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9093 |
2310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36372, 53);