Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091019 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624724 ⋊ C2 |
| derived | C32×C27 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C27 | C2×C3 |
| Frattini | C3×C9 | C3×C3⋊D3 |
| Fitting | #10624724 | C2 |
| socle | C3 | #92297 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 | |
137 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 137 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=f,d^3=f,f^3=g,b^a=bdf^2g,c^a=c^2,d^a=d^2f^2g^2,e^a=e^2,f^a=f^2g^2,g^a=g^2,c^b=ce,e^b=eg81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1093);