Finite Group DatabasebetaFinite Group Databasebeta| order | 13734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#17987082 |
| Fitting, socle | C3×C7×C109 ⋊ C2×C3 |
| derived, Hall | C7×C109 ⋊ C2×C32 |
| Hall | C3×#14556234 ⋊ C2 |
| Hall | D7×C109 ⋊ C32 |
| Sylow | C109 ⋊ C3×AGL(1,𝔽7) |
| Hall | D7 ⋊ C3×C109⋊C3 |
| Sylow | C7 ⋊ C2×C3×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #17987082 |
| commutator, cosocle, hypocenter | C7×C109 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C109 | C2×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2289 |
561 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#17987078⋊C2, #17987082⋊D3, D3×#17987082, … |
| maximal normal subgroup of | C3×#17987078⋊C2, #17987082⋊D3, D3×#17987082, … |
| maximal quotient of | C3×#22603875, C2×C3×#17987082 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13734, 46);