Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×#4208 |
| Fitting, Sylow | C9×#737 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C92 | C3⋊D3 |
| commutator, hypocenter | H(3,𝔽3) | C2×C3×C9 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | C9×#737 | C2 |
| prime radical | C3×#272 | C32 |
| cosocle | C3×H(3,𝔽3) | C2×C32 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C92 | |
434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1451);