Finite Group DatabasebetaFinite Group Databasebeta| order | 38234 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D2731⋊C7 |
| unambiguous semidirect product | (C2731⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C2731 ⋊ C2×C7 |
| Hall | C2731⋊C7 ⋊ C2 |
| Hall | D2731 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2731 | C2×C7 |
| LCS | G ▷ C2731 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2731 |
Polycyclic presentation:
2,7,2731|c^a=c^2730,c^b=c^1238209 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38234, 1);