Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C3×D32×C13 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C3×C13) |
| Fitting, socle, Hall | C33×C13 ⋊ C22 |
| derived | C32 ⋊ C22×C3×C13 |
| Sylow | C33 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D32 |
| commutator, cosocle, hypocenter | C32 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C33×C13 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C3×C13 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
351 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D32×D13 |
| maximal normal subgroup of | C3×D32×D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 207);