Finite Group DatabasebetaFinite Group Databasebeta| order | 34404 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×#6923⋊C3 |
| unambiguous semidirect product | #6923⋊(C3×C47) |
| unambiguous semidirect product | (C47×#6923)⋊C3 |
| Fitting, socle, Hall | C47×C61 ⋊ C3×C4 |
| derived, Sylow | C61 ⋊ C3×C4×C47 |
| Hall | C47×#6923 ⋊ C3 |
| Hall | C47×C61⋊C3 ⋊ C4 |
| Hall | #6923 ⋊ C3×C47 |
| Hall | C61⋊C3 ⋊ C4×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | #6923⋊C3 |
| commutator, hypocenter | C61 | C3×C4×C47 |
| Frattini | C1 | G |
| Fitting, socle | C47×C61 | C3×C4 |
| prime radical | C47×D61⋊C3 | C2 |
| cosocle | D61 | C2×C3×C47 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C47 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2867 |
799 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34404, 14);