Finite Group DatabasebetaFinite Group Databasebeta| order | 4524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic377⋊C3 |
| derived, Hall | C13×C29 ⋊ C3×C4 |
| Hall | Dic377 ⋊ C3 |
| Hall | C29×C13⋊C3 ⋊ C4 |
| Hall | C13⋊C3 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic13⋊C3 |
| Sylow | C13 ⋊ C3×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C29⋊(D13⋊C3) |
| commutator, hypocenter | C13×C29 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C29 | C2×C3 |
| prime radical | C2×C29×C13⋊C3 | C2 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 1508 |
Polycyclic presentation:
2,3,13,29,2|a^2=e,c^a=c^12,d^a=d^28,c^b=c^3212 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic377⋊C3, C3⋊(Dic377⋊C3), C5×Dic377⋊C3, … |
| maximal normal subgroup of | C3×Dic377⋊C3, C5×Dic377⋊C3, C7×Dic377⋊C3, … |
| maximal quotient of | Dic377⋊C9, C3×Dic377⋊C3, C3⋊(Dic377⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4524, 12);