Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of C3⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C3⋊#595 |
| unambiguous semidirect product | C3⋊(C72×#595) |
| Fitting, socle, Hall | C3×C72×C17 ⋊ C4 |
| derived, Hall | C3×C17 ⋊ C4×C72 |
| Hall | C72×C17 ⋊ Dic3 |
| Hall | C3×C72 ⋊ #595 |
| Sylow | C17 ⋊ C72×Dic3 |
| Sylow | C3 ⋊ C72×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C3⋊#595 |
| commutator, hypocenter | C3×C17 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C4 |
| prime radical | C3×C72×D17 | C2 |
| cosocle | C3×D17 | C2×C72 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C72 | |
120 conjugacy classes of subgroups.
882 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 144);