Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C36 |
| direct product | C33×C3⋊(C3⋊D3) |
| unambiguous semidirect product | C3⋊(C33×C3⋊D3) |
| Fitting, socle, Sylow | C36 ⋊ C2 |
| derived | C33 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C33 | C2×C33 |
| Frattini | C1 | G |
| Fitting, socle | C36 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C33 | |
29492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C3⋊#92302, C3×C3⋊#92338, #72243449, … |
| maximal normal subgroup of | C3×#11758168, C32×C3⋊#1113, C3×C3⋊((C3⋊D3)⋊H(3,𝔽3)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1798);