Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of AGL(1,ℤ/27) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10624462⋊C2 |
| Fitting, Sylow | #10624462 ⋊ C2 |
| derived | C27 ⋊ C2×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,ℤ/27) |
| commutator, hypocenter | C27 | C2×C27 |
| Frattini | C92 | C3×D3 |
| Fitting | #10624462 | C2 |
| socle | C32 | D9⋊C9 |
| prime radical | C3×D27 | C9 |
| cosocle | #6864 | C2×C3 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C3 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=e,c^3=d,d^3=f,e^3=g,c^a=c^2d^2f^2,d^a=d^2f^2,f^a=f^2,c^b=cd,d^b=df,e^c=ef^293 conjugacy classes — view the full character table.
| maximal subgroup of | #72214339, #72221799, C2×#10624462⋊C2 |
| maximal normal subgroup of | #72214339, C2×#10624462⋊C2 |
| maximal quotient of | #72221799, C2×#10624462⋊C2, #72277428 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 553);