Finite Group DatabasebetaFinite Group Databasebeta| order | 4524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊D29 |
| unambiguous semidirect product | D87⋊D13 |
| unambiguous semidirect product | D377⋊D3 |
| Fitting, socle, derived, Hall | C3×C13×C29 ⋊ C22 |
| Hall | C13×C29 ⋊ C2×D3 |
| Hall | C3×C29 ⋊ C2×D13 |
| Hall | C3×C13 ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×D13 |
| Sylow | C13 ⋊ D3×D29 |
| Sylow | C3 ⋊ D13×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C29 | C22 |
| LCS | G ▷ C3×C13×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1131 |
Polycyclic presentation:
2^2,3,13,29|d^a=d^12,e^a=e^28,c^b=c^2,d^b=d^12318 conjugacy classes — view the full character table.
| maximal subgroup of | D117⋊D29, D87⋊(D13⋊C3), C3×D39⋊D29, … |
| maximal normal subgroup of | D87⋊(D13⋊C3), C3×D39⋊D29, C5×D39⋊D29, … |
| maximal quotient of | D117⋊D29, C3×D39⋊D29, D377⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4524, 42);