Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D3×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D3×D13 |
| Fitting, socle, Hall | C33×C13 ⋊ C22 |
| derived | C3×C13 ⋊ C22×C32 |
| Sylow | C33 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D3×D13 |
| commutator, cosocle, hypocenter | C3×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C33×C13 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C32 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 234 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×D13, C32×D3×#261, D3×C3⋊(C3⋊#261), … |
| maximal normal subgroup of | D3×C3⋊D3×D13, C32×D3×#261, D3×C3⋊(C3⋊#261), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 205);