Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#19150256 |
| Fitting | C3×C19×C49 ⋊ C2×C3 |
| derived, Hall | C19×C49 ⋊ C2×C32 |
| Hall | C3×#14584108 ⋊ C2 |
| Hall | C19×D49 ⋊ C32 |
| Hall | D49 ⋊ C3×C19⋊C3 |
| Sylow | C49 ⋊ C2×C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19150256 |
| commutator, cosocle, hypocenter | C19×C49 | C2×C32 |
| Frattini | C7 | C3×#11716326 |
| Fitting | C3×C19×C49 | C2×C3 |
| socle | C3×C7×C19 | AGL(1,𝔽7) |
| LCS | G ▷ C19×C49 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2793 |
510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#19150252⋊C2, #19150256⋊D3, D3×#19150256, … |
| maximal normal subgroup of | C3×#19150252⋊C2, #19150256⋊D3, D3×#19150256, … |
| maximal quotient of | C3×#26013749, C2×C3×#19150256 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 47);