Finite Group DatabasebetaFinite Group Databasebeta| order | 1848 |
| isoclinism | isoclinic class of D7×D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D7×Dic33 |
| unambiguous semidirect product | (C3×D7)⋊Dic11 |
| unambiguous semidirect product | (C11×D7)⋊Dic3 |
| derived, Hall | C3×C7×C11 ⋊ C2×C4 |
| Hall | C7×C11 ⋊ C2×Dic3 |
| Hall | C3×C11 ⋊ C4×D7 |
| Hall | C3×C7 ⋊ C2×Dic11 |
| Sylow | C11 ⋊ Dic3×D7 |
| Sylow | C7 ⋊ C2×Dic33 |
| Sylow | C3 ⋊ D7×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D33 |
| commutator, hypocenter | C3×C7×C11 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C7×C11 | C22 |
| prime radical | C2×C3×C11×D7 | C2 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 924 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1848, 64);