Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624884 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C3×C3⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624884 | C2 |
| prime radical | #92302 | C3 |
| hypercenter | C9 | C3⋊AGL(1,ℤ/9) |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 ◁ C9 | |
296 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=f,b^a=b^2d,e^a=e^2,g^a=g^2,c^b=cf,d^b=dg,e^b=ef,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | #72277466, #72277553 |
| maximal normal subgroup of | #72277553 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1554);