Finite Group DatabasebetaFinite Group Databasebeta| order | 32754 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D309 |
| unambiguous semidirect product | C3⋊(C53×D103) |
| unambiguous semidirect product | C103⋊(D3×C53) |
| Fitting, socle, Hall | C3×C53×C103 ⋊ C2 |
| derived, Hall | C3×C103 ⋊ C2×C53 |
| Hall | C53×C103 ⋊ D3 |
| Hall | C3×C53 ⋊ D103 |
| Sylow | C103 ⋊ D3×C53 |
| Sylow | C3 ⋊ C53×D103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D309 |
| commutator, cosocle, hypocenter | C3×C103 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C53×C103 | C2 |
| LCS | G ▷ C3×C103 | |
| UCS | C1 ◁ C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16377 |
8268 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32754, 7);