Finite Group DatabasebetaFinite Group Databasebeta| order | 14049 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×C223⋊C9 |
| unambiguous semidirect product | C223⋊(C7×C9) |
| derived, Sylow | C223 ⋊ C7×C9 |
| Hall | C7×C223 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C223⋊C3 |
| commutator, hypocenter | C223 | C7×C9 |
| Frattini | C3 | C7×C223⋊C3 |
| Fitting, socle, prime radical | C3×C7×C223 | C3 |
| cosocle | C3×C223 | C3×C7 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C3×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14049 |
1617 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×C223⋊C9, C7×D223⋊C9, D7×C223⋊C9, … |
| maximal normal subgroup of | C2×C7×C223⋊C9, C7×D223⋊C9, D7×C223⋊C9, … |
| maximal quotient of | C2×C7×C223⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14049, 3);