Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, derived, Hall | C19×C49 ⋊ C2×C32 |
| Hall | C19⋊C3×C49⋊C3 ⋊ C2 |
| Hall | D19×C49 ⋊ C32 |
| Sylow | C49 ⋊ C3×D19⋊C3 |
| Hall | D19 ⋊ C3×C49⋊C3 |
| Sylow | C19 ⋊ C2×C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C19×C49 | C2×C32 |
| Frattini | C7 | ΓL(1,𝔽8)×D19⋊C3 |
| socle | C7×C19 | C2×C3×ΓL(1,𝔽8) |
| LCS | G ▷ C19×C49 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 931 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D49⋊C3, C2×D19⋊C3×C49⋊C3 |
| maximal normal subgroup of | D19⋊C3×D49⋊C3, C2×D19⋊C3×C49⋊C3 |
| maximal quotient of | C49⋊C3×(C19⋊C3)⋊C4, C2×D19⋊C3×C49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 35);