Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C7 |
| direct product | C17×C3⋊#5997 |
| unambiguous semidirect product | C3⋊(C17×#5997) |
| Fitting, socle, Hall | C3×C72×C17 ⋊ C4 |
| derived, Hall | C3×C72 ⋊ C4×C17 |
| Hall | C72×C17 ⋊ Dic3 |
| Hall | C3×C17 ⋊ #5997 |
| Sylow | C72 ⋊ Dic3×C17 |
| Sylow | C3 ⋊ C17×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊#5997 |
| commutator, hypocenter | C3×C72 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C4 |
| prime radical | C3×C17×C7⋊D7 | C2 |
| cosocle | C3×C7⋊D7 | C2×C17 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C17 | |
56 conjugacy classes of subgroups.
714 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#13183544, C17×C9⋊#5997, C17×C3⋊#10596885, … |
| maximal normal subgroup of | C17×C3⋊(#5997⋊C3), C3×C17×C3⋊#5997 |
| maximal quotient of | C17×C9⋊#5997, C3×C17×C3⋊#5997, C17×C3⋊(C3⋊#5997) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 165);