Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of C7⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C7⋊#595 |
| Fitting, socle, Hall | C3×C72×C17 ⋊ C4 |
| derived | C7×C17 ⋊ C3×C4×C7 |
| 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 | C7×C17 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C4 |
| prime radical | C3×C72×D17 | C2 |
| cosocle | C7×D17 | C2×C3×C7 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C3×C7 | |
72 conjugacy classes of subgroups.
798 conjugacy classes — view the full character table.
| maximal subgroup of | C7×(C7⋊C9)⋊#595, #44472537, #44472539, … |
| maximal normal subgroup of | C7×(C7⋊C9)⋊#595, #44472537, #44472539, … |
| maximal quotient of | C7×C9×C7⋊#595, C32×C7×C7⋊#595, C3×C7×C3⋊(C7⋊#595) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 134);