Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of D171 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D171 |
| unambiguous semidirect product | C9⋊(C72×D19) |
| unambiguous semidirect product | C19⋊(C72×D9) |
| Fitting, Hall | C72×C9×C19 ⋊ C2 |
| derived, Hall | C9×C19 ⋊ C2×C72 |
| Hall | C72×C19 ⋊ D9 |
| Hall | C72×C9 ⋊ D19 |
| Sylow | C19 ⋊ C72×D9 |
| Sylow | C9 ⋊ C72×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D171 |
| commutator, cosocle, hypocenter | C9×C19 | C2×C72 |
| Frattini | C3 | C72×D57 |
| Fitting | C72×C9×C19 | C2 |
| socle | C3×C72×C19 | D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
4263 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×D9×D19, C7×D7×D171, C7×D63⋊D19, … |
| maximal normal subgroup of | C72×D9×D19, C7×D7×D171, C7×D63⋊D19, … |
| maximal quotient of | C72×Dic171, C2×C72×D171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 156);