Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #92197 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×#92197 |
| Fitting, Sylow | C3×#6855 ⋊ C2 |
| derived | #6855 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C9⋊D9 |
| commutator, cosocle, hypocenter | #6855 | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | C3×#6855 | C2 |
| socle | C34 | C3⋊D3 |
| LCS | G ▷ #6855 | |
| UCS | C1 ◁ C32 | |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 678);