Finite Group DatabasebetaFinite Group Databasebeta| order | 1242 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D69 |
| unambiguous semidirect product | C3⋊(C32×D23) |
| unambiguous semidirect product | C23⋊(C32×D3) |
| Fitting, socle, Hall | C33×C23 ⋊ C2 |
| derived | C3×C23 ⋊ C2×C32 |
| Sylow | C33 ⋊ D23 |
| Sylow | C23 ⋊ C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D69 |
| commutator, cosocle, hypocenter | C3×C23 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C33×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C32 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 414 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1242, 25);