Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #4174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C32×#4174 |
| Fitting, Sylow | C32×AΣL(1,𝔽27) ⋊ C2 |
| derived | H(3,𝔽3) ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C33 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | C32×AΣL(1,𝔽27) | C2 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C33 | |
1388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 81 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | #72243618, C3×#13091645, C3×#13091661, … |
| maximal normal subgroup of | #72243618, C3×#13091645, C3×#13091661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1647);