Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #92344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
| direct product | C3×#92344 |
| Fitting, Sylow | C3×#6908 ⋊ C2 |
| derived | #6908 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92344 |
| commutator, cosocle, hypocenter | #6908 | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×#6908 | C2 |
| socle | C32 | C3⋊#272 |
| LCS | G ▷ #6908 | |
| UCS | C1 ◁ C3 | |
503 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 503 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #72221923, C3×#13091662, #72221964, … |
| maximal normal subgroup of | C3×#13091662, #72221964, #72222192, … |
| maximal quotient of | C2×C3×#92344 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1685);