Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | #22552712 ⋊ C2 |
| Hall | C72×D19 ⋊ C9 |
| Sylow | C72 ⋊ #4294⋊C2 |
| Hall | D19 ⋊ #89205 |
| Sylow | C19 ⋊ C2×#89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D19⋊#3862 |
| commutator, hypocenter | C72×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C2×C3 |
| prime radical | C3×C72×D19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
Polycyclic presentation:
2,3,7^2,19,3|b^3=f,e^a=e^18,c^b=c^2,d^b=d^4,e^b=e^7555 conjugacy classes — view the full character table.
| maximal subgroup of | #45691546, #45691567, #45691568, … |
| maximal normal subgroup of | #45691546, #45691567, #45691568, … |
| maximal quotient of | #45691506, C2×#30660602 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 129);