Finite Group DatabasebetaFinite Group Databasebeta| order | 1854 |
| isoclinism | isoclinic class of D103⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D103⋊C3 |
| unambiguous semidirect product | D103⋊C32 |
| unambiguous semidirect product | (C103⋊C3)⋊(C2×C3) |
| unambiguous semidirect product | (C3×D103)⋊C3 |
| Fitting, socle | C3×C103 ⋊ C2×C3 |
| derived, Sylow | C103 ⋊ C2×C32 |
| Hall | C3×C103⋊C3 ⋊ C2 |
| Hall | D103 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D103⋊C3 |
| commutator, cosocle, hypocenter | C103 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C103 | C2×C3 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 309 |
69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1854, 7);