Finite Group DatabasebetaFinite Group Databasebeta| order | 36414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | D7⋊#14579585 |
| Fitting, socle, derived, Hall | C7×C172 ⋊ C2×C9 |
| Hall | C7⋊#14579585 ⋊ C2 |
| Hall | D7×C172 ⋊ C9 |
| Sylow | C172 ⋊ D7⋊C9 |
| Hall | D7 ⋊ #14579585 |
| Sylow | C7 ⋊ C2×#14579585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C172 | C2×C9 |
| prime radical | D7×C172⋊C3 | C3 |
| cosocle | C7×C172⋊C3 | C2×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1071 |
Polycyclic presentation:
2,3^2,7,17^2|b^3=c,d^a=d^6,d^b=d^2,e^b=e^5f^11,f^b=e^7f^2,e^c=e^12f,f^c=e^13f^4181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36414, 67);