Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #22603530⋊C2 |
| unambiguous semidirect product | #22603534⋊C2 |
| unambiguous semidirect product | #22603536⋊C2 |
| Fitting, derived, Hall | C31×C49 ⋊ C22×C3 |
| Hall | D31×D49 ⋊ C3 |
| Hall | #17986946 ⋊ C22 |
| Sylow | C49 ⋊ C2×D31⋊C3 |
| Sylow | C31 ⋊ C2×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C49 | C22×C3 |
| Frattini | C7 | #13049955⋊C2 |
| socle | C7×C31 | C2×AGL(1,𝔽7) |
| LCS | G ▷ C31×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1519 |
Polycyclic presentation:
2^2,3,7,31,7|d^7=f^6,e^a=e^30,d^b=d^6f,f^b=f^6,d^c=d^2f^3,e^c=e^25,f^c=f^2158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 27);