Finite Group DatabasebetaFinite Group Databasebeta| order | 34554 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×D443⋊C13 |
| unambiguous semidirect product | D443⋊(C3×C13) |
| unambiguous semidirect product | (C3×D443)⋊C13 |
| unambiguous semidirect product | (C443⋊C13)⋊(C2×C3) |
| Fitting, socle, Hall | C3×C443 ⋊ C2×C13 |
| derived, Sylow | C443 ⋊ C2×C3×C13 |
| Hall | C3×C443⋊C13 ⋊ C2 |
| Hall | C443⋊C13 ⋊ C2×C3 |
| Hall | C3×D443 ⋊ C13 |
| Hall | D443 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D443⋊C13 |
| commutator, cosocle, hypocenter | C443 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C443 | C2×C13 |
| LCS | G ▷ C443 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1329 |
129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34554, 11);