Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | C19×#89205 ⋊ C2 |
| Hall | C7⋊D133 ⋊ C9 |
| Hall | #89205 ⋊ D19 |
| Sylow | C72 ⋊ C9×D19 |
| Sylow | C19 ⋊ #11725078 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #19150292 |
| commutator, hypocenter | C72×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C2×C3 |
| prime radical | C3×C7⋊D133 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
Polycyclic presentation:
2,3,7^2,19,3|b^3=f,c^a=c^6,d^a=d^6,e^a=e^18,c^b=c^2,d^b=d^4555 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#11725078, #11725075⋊D19, #11725071⋊D19, … |
| maximal normal subgroup of | D19×#11725078, #11725075⋊D19, #11725071⋊D19, … |
| maximal quotient of | #45691484, C2×#30660580 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 107);