Finite Group DatabasebetaFinite Group Databasebeta| order | 34132 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×Dic161 |
| unambiguous semidirect product | C7⋊(C53×Dic23) |
| unambiguous semidirect product | C23⋊(Dic7×C53) |
| derived, Hall | C7×C23 ⋊ C4×C53 |
| Hall | C7×C23×C53 ⋊ C4 |
| Hall | C23×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic7×C53 |
| Sylow | C7 ⋊ C53×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D161 |
| commutator, hypocenter | C7×C23 | C4×C53 |
| Frattini | C2 | C53×D161 |
| Fitting, socle, prime radical | C2×C7×C23×C53 | C2 |
| cosocle | C2×C7×C23 | C2×C53 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C2×C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34132 |
8692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34132, 7);