Finite Group DatabasebetaFinite Group Databasebeta| order | 18732 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×C22⋊(C223⋊C3) |
| unambiguous semidirect product | C22⋊(C7×C223⋊C3) |
| unambiguous semidirect product | C223⋊(C7×A4) |
| Fitting, socle, Hall | C22×C7×C223 ⋊ C3 |
| derived, Hall | C22×C223 ⋊ C3×C7 |
| Hall | C7×C223 ⋊ A4 |
| Sylow | C223 ⋊ C7×A4 |
| Hall | C22×C7 ⋊ C223⋊C3 |
| Sylow | C22 ⋊ C7×C223⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C22⋊(C223⋊C3) |
| commutator, cosocle, hypocenter | C22×C223 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C223 | C3 |
| LCS | G ▷ C22×C223 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6244 |
2100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18732, 52);