Finite Group DatabasebetaFinite Group Databasebeta| order | 32148 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C47⋊((C19⋊C3)⋊C4)) |
| unambiguous semidirect product | C47⋊(C3⋊((C19⋊C3)⋊C4)) |
| unambiguous semidirect product | (C19⋊C3)⋊Dic141 |
| unambiguous semidirect product | Dic2679⋊C3 |
| derived | C3×C19×C47 ⋊ C3×C4 |
| Hall | C3×C47×C19⋊C3 ⋊ C4 |
| Hall | C19×C47 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ Dic47 |
| Sylow | C47 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3×Dic141 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C47⋊(D19⋊C3)) |
| commutator, hypocenter | C3×C19×C47 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C19×C47 | C2×C3 |
| prime radical | C2×C3×C47×C19⋊C3 | C2 |
| LCS | G ▷ C3×C19×C47 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10716 |
Polycyclic presentation:
2,3^2,19,47,2|a^2=f,c^a=c^2,d^a=d^18,e^a=e^46,d^b=d^71278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32148, 44);