Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C19 ⋊ C3×D3 |
| derived | C19×#3862 ⋊ C2×C3 |
| Hall | C19×ΓL(1,𝔽8)2 ⋊ C2 |
| Hall | ΓL(1,𝔽8)2 ⋊ D19 |
| Sylow | C72 ⋊ C3×D57 |
| Sylow | C19 ⋊ #64418⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×#3862 | C2×C3 |
| Fitting, socle | C72×C19 | C3×D3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2,3^2,19,7^2|c^a=c^2,d^a=d^18,e^a=e^2f^3,f^a=e^6f^5,e^b=e^4,f^b=f^4,e^c=e^4f^4,f^c=f^2245 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#64418⋊C3, (#64418⋊C3)⋊D19, #45692008, … |
| maximal normal subgroup of | D19×#64418⋊C3, (#64418⋊C3)⋊D19, #45692008, … |
| maximal quotient of | #45691813, C2×#30660729 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 256);