Finite Group DatabasebetaFinite Group Databasebeta| order | 1272 |
| isoclinism | isoclinic class of D3×#6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×#6157 |
| unambiguous semidirect product | (C3×#6157)⋊C2 |
| unambiguous semidirect product | (C3⋊#6157)⋊C2 |
| Fitting, socle, derived, Hall | C3×C53 ⋊ C2×C4 |
| Sylow | C53 ⋊ C4×D3 |
| Sylow | C3 ⋊ C2×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C53 | C2×C4 |
| prime radical | D3×D53 | C2 |
| cosocle | C3×D53 | C22 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 56 |
| transitive degree | μt(G) = 159 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽53) |
| maximal normal subgroup of | D3×AGL(1,𝔽53) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1272, 33);