Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3×C22⋊(C52⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | D3×C22⋊(C52⋊C3) |
| unambiguous semidirect product | C3⋊(C2×C22⋊(C52⋊C3)) |
| unambiguous semidirect product | (C22×D3)⋊(C52⋊C3) |
| unambiguous semidirect product | (C52×D3)⋊A4 |
| Fitting, socle, derived | C22×C3×C52 ⋊ C2×C3 |
| Sylow | C52 ⋊ D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C3×C52 | C2×C3 |
| LCS | G ▷ C22×C3×C52 | |
| UCS | C1 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 702);