Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C2×AΣL(1,𝔽27)⋊C9 |
| unambiguous semidirect product | (C2×AΣL(1,𝔽27))⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C3×H(3,𝔽3) |
| commutator | C32 | C2×C32×C9 |
| Frattini, cosocle | C33 | C2×C33 |
| prime radical | C2×C3×AΣL(1,𝔽27) | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32×C9 ◁ G | |
304 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 280);