Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×Dic37⋊C3 |
| unambiguous semidirect product | Dic37⋊(C3×C73) |
| derived, Sylow | C37 ⋊ C3×C4×C73 |
| Hall | C73×Dic37 ⋊ C3 |
| Hall | C73×C37⋊C3 ⋊ C4 |
| Hall | C37×C73 ⋊ C3×C4 |
| Hall | Dic37 ⋊ C3×C73 |
| Hall | C37⋊C3 ⋊ C4×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C73 | D37⋊C3 |
| commutator, hypocenter | C37 | C3×C4×C73 |
| Frattini | C2 | C73×D37⋊C3 |
| Fitting, socle | C2×C37×C73 | C2×C3 |
| prime radical | C2×C73×C37⋊C3 | C2 |
| cosocle | C2×C37 | C2×C3×C73 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C73 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10804 |
1752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 18);