Finite Group DatabasebetaFinite Group Databasebeta| order | 29756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽173) |
| unambiguous semidirect product | #10621924⋊C43 |
| Fitting, socle, derived, Sylow | C173 ⋊ C4×C43 |
| Hall | C173⋊C43 ⋊ C4 |
| Hall | #10621924 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C173 | C4×C43 |
| prime radical | D173⋊C43 | C2 |
| cosocle | D173 | C2×C43 |
| LCS | G ▷ C173 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,43,2,173|a^2=c,d^a=d^93,d^b=d^16,d^c=d^172173 conjugacy classes — view the full character table.
| holomorph of | C173 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29756, 8);