Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #10624557 ⋊ C2 |
| derived | C32⋊C9 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #4207 |
| commutator, hypocenter | C32⋊C9 | C2×C9 |
| Frattini, socle | C33 | C3×C3⋊D3 |
| Fitting | #10624557 | C2 |
| prime radical | C3×#4181 | C3 |
| cosocle | C3×C32⋊C9 | C2×C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C32 | |
206 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=g,d^3=e,b^a=b^2c^2e^2,d^a=d^2e^2,e^a=e^2,c^b=ce,d^b=df117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 723);