Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C32 |
| Hall | #22552728 ⋊ C2 |
| Hall | C72×D19 ⋊ C32 |
| Sylow | C72 ⋊ C3×D19⋊C3 |
| Hall | D19 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C19 ⋊ C2×ΓL(1,𝔽8)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C19 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 399 |
Polycyclic presentation:
2,3^2,7^2,19|f^a=f^18,d^b=d^2,f^b=f^11,d^c=d^4,e^c=e^2107 conjugacy classes — view the full character table.
| maximal subgroup of | #45691991, #45692020, #45692028, … |
| maximal normal subgroup of | #45691991, #45692020, #45692028, … |
| maximal quotient of | #45691798, C2×#30660714 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 241);