Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D3×C3⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×C3⋊(D13⋊C3) |
| unambiguous semidirect product | (C3×D3)⋊(D13⋊C3) |
| unambiguous semidirect product | (D3×C13⋊C3)⋊D3 |
| unambiguous semidirect product | (D3×D39)⋊C3 |
| Fitting, socle, derived | C32×C13 ⋊ C22×C3 |
| Hall | C32×C13⋊C3 ⋊ C22 |
| Sylow | C13 ⋊ C3×D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13 | C22×C3 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 | |
108 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 78 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D13⋊C3, C2×D3×C3⋊(D13⋊C3), S4×C3⋊(D13⋊C3), … |
| maximal normal subgroup of | D32×D13⋊C3, C2×D3×C3⋊(D13⋊C3) |
| maximal quotient of | #72241936, C2×D3×C3⋊(D13⋊C3), #72241981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 187);