Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #22604103⋊C2 |
| unambiguous semidirect product | #22604105⋊C2 |
| unambiguous semidirect product | #22604109⋊C2 |
| Fitting, socle, derived, Hall | C7×C73 ⋊ C22×C9 |
| Hall | #17987164 ⋊ C22 |
| Hall | D7×D73 ⋊ C9 |
| Sylow | C73 ⋊ C2×D7⋊C9 |
| Sylow | C7 ⋊ C2×#10620323⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C22×C9 |
| prime radical | D7×D73⋊C3 | C3 |
| cosocle | C7×C73⋊C3 | C22×C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 511 |
Polycyclic presentation:
2^2,3^2,7,73|c^3=d,f^a=f^72,e^b=e^6,e^c=e^2,f^c=f^4,f^d=f^6462 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 142);