Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
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 ⋊ #11725075 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C2×C9 |
| prime radical | C7×(C19⋊C3)⋊D7 | C3 |
| cosocle | C72×C19⋊C3 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
Polycyclic presentation:
2,3^2,7^2,19|b^3=c,d^a=d^6,f^a=f^18,d^b=d^2,e^b=e^4,f^b=f^16,f^c=f^11100 conjugacy classes — view the full character table.
| maximal subgroup of | #45692085, #45692088, #45692090, … |
| maximal normal subgroup of | #45692085, #45692088, #45692090, … |
| maximal quotient of | #45691778, C2×#30660694 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 221);