Finite Group DatabasebetaFinite Group Databasebeta| order | 4524 |
| automorphism | Aut(G) order 1520064 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1131 |
| unambiguous semidirect product | C3⋊Dic377 |
| derived, Hall | C3×C13×C29 ⋊ C4 |
| Hall | C13×C29 ⋊ Dic3 |
| Hall | C3×C29 ⋊ Dic13 |
| Hall | C3×C13 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic39 |
| Sylow | C13 ⋊ Dic87 |
| Sylow | C3 ⋊ Dic377 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1131 |
| commutator, hypocenter | C3×C13×C29 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C13×C29 | C2 |
| LCS | G ▷ C3×C13×C29 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4524 |
Polycyclic presentation:
2,3,13,29,2|a^2=e,b^a=b^2,c^a=c^12,d^a=d^281134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3393, C3⋊(Dic377⋊C3), C3×Dic1131, … |
| maximal normal subgroup of | C3⋊(Dic377⋊C3), C3×Dic1131, C5×Dic1131, … |
| maximal quotient of | Dic3393, C3×Dic1131, C3⋊Dic1131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4524, 9);