Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D111⋊D73 |
| unambiguous semidirect product | D219⋊D37 |
| unambiguous semidirect product | D2701⋊D3 |
| Fitting, socle, derived, Hall | C3×C37×C73 ⋊ C22 |
| Hall | C37×C73 ⋊ C2×D3 |
| Hall | C3×C73 ⋊ C2×D37 |
| Hall | C3×C37 ⋊ C2×D73 |
| Sylow | C73 ⋊ D3×D37 |
| Sylow | C37 ⋊ D3×D73 |
| Sylow | C3 ⋊ D37×D73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C37×C73 | C22 |
| LCS | G ▷ C3×C37×C73 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8103 |
Polycyclic presentation:
2^2,3,37,73|d^a=d^36,e^a=e^72,c^b=c^2,d^b=d^362112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 84);