Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#13049954⋊C2 |
| unambiguous semidirect product | #13049954⋊(C2×C7) |
| unambiguous semidirect product | #13049958⋊(C2×C7) |
| unambiguous semidirect product | #13049960⋊(C2×C7) |
| Fitting, socle, Hall | C72×C31 ⋊ C22×C3 |
| derived | C7×C31 ⋊ C22×C3×C7 |
| Hall | C7×D7×D31 ⋊ C3 |
| Hall | C7×#10620252 ⋊ C22 |
| Sylow | C72 ⋊ C2×D31⋊C3 |
| Sylow | C31 ⋊ C2×C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13049954⋊C2 |
| commutator, cosocle, hypocenter | C7×C31 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C31 | C22×C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C7 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1302 |
273 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 142);