Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091647 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624930 ⋊ C2 |
| derived | C3×AΣL(1,𝔽27) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×AΣL(1,𝔽27) | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | #10624930 | C2 |
| socle | C3 | C3×C3⋊#272 |
| LCS | G ▷ C3×AΣL(1,𝔽27) | |
| UCS | C1 | |
536 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|b^a=b^2,c^a=c^2,e^a=e^2,f^a=fg^2,g^a=g^2,c^b=cf,f^b=fg,e^d=eg66 conjugacy classes — view the full character table.
| maximal subgroup of | #72221901, C3×#13091647, #72221905, … |
| maximal normal subgroup of | C3×#13091647, #72221905, #72221929, … |
| maximal quotient of | C3×#13091647, #72243671, C2×#13091647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1721);