Finite Group DatabasebetaFinite Group Databasebeta| order | 34356 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#13109888⋊C3 |
| unambiguous semidirect product | #13109888⋊(C3×C7) |
| Fitting, socle, Hall | C7×C409 ⋊ C3×C4 |
| derived, Sylow | C409 ⋊ C3×C4×C7 |
| Hall | C7×#13109888 ⋊ C3 |
| Hall | C7×C409⋊C3 ⋊ C4 |
| Hall | #13109888 ⋊ C3×C7 |
| Hall | C409⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13109888⋊C3 |
| commutator, hypocenter | C409 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C409 | C3×C4 |
| prime radical | C7×D409⋊C3 | C2 |
| cosocle | D409 | C2×C3×C7 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2863 |
322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34356, 26);