Finite Group DatabasebetaFinite Group Databasebeta| order | 36414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×D63 |
| unambiguous semidirect product | C7⋊(C172×D9) |
| unambiguous semidirect product | C9⋊(D7×C172) |
| Fitting, Hall | C7×C9×C172 ⋊ C2 |
| derived, Hall | C7×C9 ⋊ C2×C172 |
| Hall | C9×C172 ⋊ D7 |
| Hall | C7×C172 ⋊ D9 |
| Sylow | C9 ⋊ D7×C172 |
| Sylow | C7 ⋊ C172×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C172 | D63 |
| commutator, cosocle, hypocenter | C7×C9 | C2×C172 |
| Frattini | C3 | C172×D21 |
| Fitting | C7×C9×C172 | C2 |
| socle | C3×C7×C172 | D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C172 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18207 |
9537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36414, 52);