Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C19×C49 ⋊ C2×C9 |
| Hall | #22552697 ⋊ C2 |
| Hall | C19×D49 ⋊ C9 |
| Hall | D49 ⋊ #4296 |
| Sylow | C49 ⋊ C2×#4296 |
| Sylow | C19 ⋊ D49⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C19×C49 | C2×C9 |
| Frattini | C7 | #14558804 |
| socle | C7×C19 | D7⋊C9 |
| prime radical | C19⋊C3×D49 | C3 |
| cosocle | C49×C19⋊C3 | C2×C3 |
| LCS | G ▷ C19×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 931 |
Polycyclic presentation:
2,3^2,7,19,7|b^3=c,d^7=f^6,d^a=d^6f,f^a=f^6,d^b=d^2f^3,e^b=e^16,f^b=f^2,e^c=e^1194 conjugacy classes — view the full character table.
| maximal subgroup of | #30660501⋊C2, C2×#30660503 |
| maximal normal subgroup of | #30660501⋊C2, C2×#30660503 |
| maximal quotient of | #45691272, C2×#30660503 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 30);