Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C7 |
| direct product | C17×C3⋊(C7⋊Dic7) |
| unambiguous semidirect product | C3⋊(C17×C7⋊Dic7) |
| unambiguous semidirect product | C7⋊(C17×Dic21) |
| derived, Hall | C3×C72 ⋊ C4×C17 |
| Hall | C3×C72×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ Dic3 |
| Hall | C3×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic3×C17 |
| Sylow | C3 ⋊ C17×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | C3⋊(C7⋊D7) |
| commutator, hypocenter | C3×C72 | C4×C17 |
| Frattini | C2 | C17×C3⋊(C7⋊D7) |
| Fitting, socle, prime radical | C2×C3×C72×C17 | C2 |
| cosocle | C2×C3×C72 | C2×C17 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2×C17 | |
120 conjugacy classes of subgroups.
2550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 73);