Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19150308 |
| Fitting, socle, derived | C3×C72×C19 ⋊ C2×C3 |
| Hall | C3×C7×#87704 ⋊ C2 |
| Hall | C72×C19 ⋊ C3×D3 |
| Sylow | C72 ⋊ D3×C19⋊C3 |
| Sylow | C19 ⋊ C3⋊(ΓL(1,𝔽8)⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C2×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
Polycyclic presentation:
2,3^2,7^2,19|c^a=c^2,d^a=d^6,e^a=e^6,d^b=d^2,f^b=f^7507 conjugacy classes — view the full character table.
| maximal subgroup of | #11716321⋊D21, #45692311, D3×#19150308, … |
| maximal normal subgroup of | #11716321⋊D21, #45692311, D3×#19150308, … |
| maximal quotient of | C3⋊#26013841, C2×C3⋊#19150308 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 370);