Finite Group DatabasebetaFinite Group Databasebeta| order | 35724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C229 ⋊ C3×C4 |
| Hall | C13×Dic229 ⋊ C3 |
| Hall | #22581986 ⋊ C4 |
| Hall | Dic229 ⋊ C13⋊C3 |
| Sylow | C229 ⋊ C4×C13⋊C3 |
| Sylow | C13 ⋊ Dic229⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31821824 |
| commutator, hypocenter | C13×C229 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C229 | C2×C3 |
| prime radical | C2×#22581986 | C2 |
| LCS | G ▷ C13×C229 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11908 |
Polycyclic presentation:
2,3,13,229,2|a^2=e,d^a=d^228,c^b=c^3,d^b=d^1341016 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35724, 15);