Finite Group DatabasebetaFinite Group Databasebeta| order | 11628 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C19⋊C3)⋊#595) |
| unambiguous semidirect product | (C19⋊C3)⋊(C3⋊#595) |
| unambiguous semidirect product | (C3⋊(C19⋊#595))⋊C3 |
| Fitting, socle, derived | C3×C17×C19 ⋊ C3×C4 |
| Hall | C3×C17×C19⋊C3 ⋊ C4 |
| Hall | C17×C19 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ #595 |
| Sylow | C19 ⋊ C3×C3⋊#595 |
| Sylow | C17 ⋊ C3⋊((C19⋊C3)⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C19 | C3×C4 |
| prime radical | C3×D17×C19⋊C3 | C2 |
| cosocle | C3×C19×D17 | C2×C3 |
| LCS | G ▷ C3×C17×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,17,19|a^2=c,d^a=d^2,e^a=e^13,f^a=f^18,f^b=f^7,e^c=e^16144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11628, 76);