Finite Group DatabasebetaFinite Group Databasebeta| order | 32542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D307 |
| unambiguous semidirect product | C307⋊(C2×C53) |
| Fitting, socle, Hall | C53×C307 ⋊ C2 |
| derived, Sylow | C307 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D307 |
| commutator, cosocle, hypocenter | C307 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C53×C307 | C2 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C53 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16271 |
8215 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32542, 2);