Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊(C3⋊(C7⋊D133)) |
| unambiguous semidirect product | C7⋊(C3⋊D399) |
| unambiguous semidirect product | C19⋊(C3⋊(C3⋊(C7⋊D7))) |
| Fitting, socle, derived, Hall | C32×C72×C19 ⋊ C2 |
| Hall | C72×C19 ⋊ C3⋊D3 |
| Hall | C32×C72 ⋊ D19 |
| Hall | C32×C19 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3⋊D57 |
| Sylow | C19 ⋊ C3⋊(C3⋊(C7⋊D7)) |
| Sylow | C32 ⋊ C7⋊D133 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72×C19 | C2 |
| LCS | G ▷ C32×C72×C19 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
Polycyclic presentation:
2,3^2,7^2,19|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^184191 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D399, D3×C3⋊(C7⋊D133), D57×C3⋊(C7⋊D7), … |
| maximal normal subgroup of | D21×D399, D3×C3⋊(C7⋊D133), D57×C3⋊(C7⋊D7), … |
| maximal quotient of | C3⋊(C3⋊(C7⋊Dic133)), C2×C3⋊(C3⋊(C7⋊D133)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 402);