Finite Group DatabasebetaFinite Group Databasebeta| order | 35724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #31821824⋊C2 |
| unambiguous semidirect product | #31821828⋊C2 |
| unambiguous semidirect product | #31821832⋊C2 |
| Fitting, socle, derived, Hall | C13×C229 ⋊ C22×C3 |
| Hall | D13×D229 ⋊ C3 |
| Hall | #22581986 ⋊ C22 |
| Sylow | C229 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ C2×D229⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C229 | C22×C3 |
| LCS | G ▷ C13×C229 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2977 |
Polycyclic presentation:
2^2,3,13,229|e^a=e^228,d^b=d^12,d^c=d^3,e^c=e^134320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35724, 41);