Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D3×D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×D39 |
| unambiguous semidirect product | (C3×D3)⋊(C3×D13) |
| Fitting, socle, Hall | C33×C13 ⋊ C22 |
| derived | C32×C13 ⋊ C22×C3 |
| Sylow | C33 ⋊ C2×D13 |
| Sylow | C13 ⋊ C3×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D39 |
| commutator, cosocle, hypocenter | C32×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C33×C13 | C22 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C3 | |
108 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 156 |
189 conjugacy classes — view the full character table.
| 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, 208);