Finite Group DatabasebetaFinite Group Databasebeta| order | 29756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic173⋊C43 |
| derived, Sylow | C173 ⋊ C4×C43 |
| Hall | C173⋊C43 ⋊ C4 |
| Hall | Dic173 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D173⋊C43 |
| commutator, hypocenter | C173 | C4×C43 |
| Fitting, socle, cosocle | C2×C173 | C2×C43 |
| prime radical | C2×C173⋊C43 | C2 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,43,173,2|a^2=d,c^a=c^172,c^b=c^16176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29756, 2);