Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C32×#4208 |
| Fitting, Sylow | C32×#737 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C9 | C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C33 |
| Frattini | C3 | C33×C3⋊D3 |
| Fitting | C32×#737 | C2 |
| socle | C33 | C3×C3⋊D3 |
| prime radical | C32×#272 | C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C32×C9 | |
1868 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, 1775);