Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×C7⋊(C7⋊#595) |
| Fitting, socle, Hall | C3×C72×C17 ⋊ C4 |
| derived, Hall | C72×C17 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ #595 |
| Hall | C3×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C3×#595 |
| Sylow | C17 ⋊ C3×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C7⋊(C7⋊#595) |
| commutator, hypocenter | C72×C17 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C4 |
| prime radical | C3×C72×D17 | C2 |
| cosocle | C72×D17 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 136);