Finite Group DatabasebetaFinite Group Databasebeta| order | 1272 |
| isoclinism | isoclinic class of D3×D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×D53 |
| unambiguous semidirect product | (D3×C53)⋊C22 |
| unambiguous semidirect product | (C3×D53)⋊C22 |
| unambiguous semidirect product | D159⋊C22 |
| Fitting, socle | C2×C3×C53 ⋊ C22 |
| derived, Hall | C3×C53 ⋊ C23 |
| Sylow | C53 ⋊ C22×D3 |
| Sylow | C3 ⋊ C22×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D53 |
| commutator, cosocle, hypocenter | C3×C53 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C53 | C22 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 318 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1272, 39);