Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×D147 |
| unambiguous semidirect product | (C3×D31)⋊D49 |
| unambiguous semidirect product | (C49×D31)⋊D3 |
| Fitting, derived, Hall | C3×C31×C49 ⋊ C22 |
| Hall | C31×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×D31 |
| Hall | C3×C31 ⋊ C2×D49 |
| Sylow | C49 ⋊ D3×D31 |
| Sylow | C31 ⋊ C2×D147 |
| Sylow | C3 ⋊ D31×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C31×C49 | C22 |
| Frattini | C7 | D21×D31 |
| socle | C3×C7×C31 | C2×D7 |
| LCS | G ▷ C3×C31×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4557 |
1275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 44);