Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #13049955⋊D7 |
| Fitting, socle, derived, Hall | C72×C31 ⋊ C22×C3 |
| Hall | D31×C7⋊D7 ⋊ C3 |
| Hall | C7×#10620253 ⋊ C22 |
| Sylow | C72 ⋊ C2×D31⋊C3 |
| Sylow | C31 ⋊ C2×ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C31 | C22×C3 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 651 |
Polycyclic presentation:
2^2,3,7^2,31|f^a=f^30,d^b=d^6,e^b=e^6,d^c=d^2,f^c=f^25174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 186);