Finite Group DatabasebetaFinite Group Databasebeta| order | 14508 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| derived, Hall | C13×C31 ⋊ C32×C4 |
| Hall | C13⋊C3×C31⋊C3 ⋊ C4 |
| Hall | Dic403 ⋊ C32 |
| Sylow | C31 ⋊ C3×Dic13⋊C3 |
| Sylow | C13 ⋊ C3×(C31⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C13⋊C3)⋊(D31⋊C3) |
| commutator, hypocenter | C13×C31 | C32×C4 |
| Fitting, socle, cosocle | C2×C13×C31 | C2×C32 |
| prime radical | C2×C13⋊C3×C31⋊C3 | C2 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1612 |
Polycyclic presentation:
2,3^2,13,31,2|a^2=f,d^a=d^12,e^a=e^30,e^b=e^5,d^c=d^3118 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14508, 78);