Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×#11765919 |
| Fitting, socle, Hall | C2×C7×C127 ⋊ C9 |
| derived, Sylow | C127 ⋊ C2×C7×C9 |
| Hall | C7×C127 ⋊ C2×C9 |
| Hall | C2×C127 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | #11765919 |
| commutator, hypocenter | C127 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C127 | C9 |
| prime radical | C2×C7×C127⋊C3 | C3 |
| cosocle | C127⋊C3 | C2×C3×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
322 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11765919⋊C4, #11765919⋊Dic7, Dic7×#11765919, … |
| maximal normal subgroup of | C7×#11765919⋊C4, #11765919⋊Dic7, Dic7×#11765919, … |
| maximal quotient of | C4×C7×#11765919, C22×C7×#11765919 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 55);