Finite Group DatabasebetaFinite Group Databasebeta| order | 36414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C17 |
| direct product | C2×C7×#14579583 |
| derived, Sylow | C172 ⋊ C2×C7×C9 |
| Hall | C2×C7×C172 ⋊ C9 |
| Hall | C7×C172 ⋊ C2×C9 |
| Hall | C2×C172 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | C172⋊C3 |
| commutator, hypocenter | C172 | C2×C7×C9 |
| Frattini | C3 | C2×C7×C172⋊C3 |
| Fitting, socle, prime radical | C2×C3×C7×C172 | C3 |
| cosocle | C3×C172 | C2×C3×C7 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2×C3×C7 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
4158 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36414, 49);