Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | #22552721 ⋊ C2 |
| Hall | C7⋊D133 ⋊ C9 |
| Sylow | C72 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ #11725078 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C2×C9 |
| prime radical | (C19⋊C3)⋊(C7⋊D7) | C3 |
| cosocle | C72×C19⋊C3 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 399 |
Polycyclic presentation:
2,3^2,7^2,19|b^3=c,d^a=d^6,e^a=e^6,f^a=f^18,d^b=d^2,e^b=e^4,f^b=f^4,f^c=f^791 conjugacy classes — view the full character table.
| maximal subgroup of | #45692088, #45692089, #45692095, … |
| maximal normal subgroup of | #45692088, #45692089, #45692095, … |
| maximal quotient of | #45691737, C2×#30660653 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 180);