Finite Group DatabasebetaFinite Group Databasebeta| order | 1272 |
| isoclinism | isoclinic class of D159 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#88322 |
| derived, Hall | C3×C53 ⋊ C8 |
| Sylow | C53 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ #88322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D159 |
| commutator, hypocenter | C3×C53 | C8 |
| Fitting, cosocle | C3×C4×C53 | C2 |
| socle, prime radical | C2×C3×C53 | C4 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 1272 |
Polycyclic presentation:
2^3,3,53|a^2=b,b^2=c,d^a=d^2,e^a=e^52324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1272, 3);