Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#22547883 |
| Fitting, socle, Hall | C2×C7×C127 ⋊ C9 |
| derived, Hall | C7×C127 ⋊ C2×C9 |
| Hall | C2×C127 ⋊ C7⋊C9 |
| Sylow | C127 ⋊ C2×C7⋊C9 |
| Hall | C2×C7 ⋊ #11765919 |
| Sylow | C7 ⋊ C2×#11765919 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22547883 |
| commutator, hypocenter | C7×C127 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C127 | C9 |
| prime radical | C2×C7×C127⋊C3 | C3 |
| cosocle | C7×C127⋊C3 | C2×C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
226 conjugacy classes — view the full character table.
| maximal subgroup of | #44544706, #44544708, #44544712, … |
| maximal normal subgroup of | #44544706, #44544708, #44544712, … |
| maximal quotient of | C4×#22547883, C22×#22547883 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 56);