Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #92297 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
| direct product | C3×#92297 |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C2 |
| derived | C32×C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92297 |
| commutator, cosocle, hypocenter | C32×C9 | C2×C32 |
| Frattini | C32 | C32×C3⋊D3 |
| Fitting | C3×C9×H(3,𝔽3) | C2 |
| socle | C33 | C3×C3⋊D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
608 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13091513, #72243534, #72243893, … |
| maximal normal subgroup of | C3×#13091513, #72243893, #72243912, … |
| maximal quotient of | #72243465, #72243912 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1434);