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 | Dic13×C229 ⋊ C3 |
| Hall | #22581985 ⋊ C4 |
| Sylow | C229 ⋊ Dic13⋊C3 |
| Hall | Dic13 ⋊ C229⋊C3 |
| Sylow | C13 ⋊ C4×C229⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31821829 |
| commutator, hypocenter | C13×C229 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C229 | C2×C3 |
| prime radical | C2×#22581985 | 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,c^a=c^12,c^b=c^3,d^b=d^941232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35724, 20);