Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | C3×C3⋊#4174 |
| unambiguous semidirect product | C3⋊(C3×#4174) |
| Fitting, Sylow | C32×AΣL(1,𝔽27) ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C32×C3⋊D3 |
| Fitting | C32×AΣL(1,𝔽27) | C2 |
| socle | C33 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
998 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | #72221865, C3×#13091105, #72221880, … |
| maximal normal subgroup of | #72221880, #72221894, #72221928, … |
| maximal quotient of | #72222306, C2×C3×C3⋊#4174, #72277559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1648);