Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #4179⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C34 |
| direct product | C3×#4179⋊C3 |
| unambiguous semidirect product | #4179⋊C32 |
| Fitting, Sylow | C3×#6911 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4179⋊C3 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | C3×#6911 | C2 |
| socle | C32 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
512 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13091660, C3×#13091110, #72243680, … |
| maximal normal subgroup of | #72243785, C3×(#4178⋊C2)⋊C3, D3×#4179⋊C3, … |
| maximal quotient of | #72277487 |
| automorphism group of | #6878 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1702);