Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C35 |
| direct product | D3×H(5,𝔽3) |
| unambiguous semidirect product | C3⋊(C2×H(5,𝔽3)) |
| Fitting, Sylow | C3×H(5,𝔽3) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C34×D3 |
| commutator, socle, cosocle | C32 | C2×C34 |
| Fitting | C3×H(5,𝔽3) | C2 |
| hypercenter | H(5,𝔽3) | D3 |
| hypocenter | C3 | C2×H(5,𝔽3) |
| LCS | G ▷ C32 ▷ C3 | |
| UCS | C1 ◁ C3 ◁ H(5,𝔽3) | |
2573 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
249 conjugacy classes — view the full character table.
| maximal subgroup of | #72243622, D3×#10624930, D3×#92392, … |
| maximal normal subgroup of | D3×#10624930, D3×#92392, D3×#92391 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1781);