Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×D57 |
| unambiguous semidirect product | C3⋊(C3×C72×D19) |
| Fitting, socle, Hall | C32×C72×C19 ⋊ C2 |
| derived | C3×C19 ⋊ C2×C3×C72 |
| Hall | C72×C19 ⋊ C3×D3 |
| Hall | C32×C72 ⋊ D19 |
| Hall | C32×C19 ⋊ C2×C72 |
| Sylow | C19 ⋊ C3×D3×C72 |
| Sylow | C32 ⋊ C72×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | D57 |
| commutator, cosocle, hypocenter | C3×C19 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C19 | C2 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C3×C72 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5586 |
4410 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C72×D19, C3×C7×D7×D57, C3×C7×D21⋊D19, … |
| maximal normal subgroup of | C3×D3×C72×D19, C3×C7×D7×D57, C3×C7×D21⋊D19, … |
| maximal quotient of | C3×C72×Dic57, C2×C3×C72×D57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 412);