Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#5997⋊C3 |
| unambiguous semidirect product | #5997⋊(C3×C17) |
| unambiguous semidirect product | (C17×#5997)⋊C3 |
| Fitting, socle, Hall | C72×C17 ⋊ C3×C4 |
| derived, Sylow | C72 ⋊ C3×C4×C17 |
| Hall | C17×#5997 ⋊ C3 |
| Hall | C17×#3861 ⋊ C4 |
| Hall | #5997 ⋊ C3×C17 |
| Hall | #3861 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #5997⋊C3 |
| commutator, hypocenter | C72 | C3×C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C17 | C3×C4 |
| prime radical | C17×#64424 | C2 |
| cosocle | C7⋊D7 | C2×C3×C17 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C17 | |
56 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#10596885⋊C3, C3×C17×#5997⋊C3, C17×C3⋊(#5997⋊C3) |
| maximal normal subgroup of | C3×C17×#5997⋊C3 |
| maximal quotient of | C17×#5997⋊C9, C3×C17×#5997⋊C3, C17×C3⋊(#5997⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 111);