Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C3⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C2×C32×C13 ⋊ C2×C3 |
| derived | C3×C13 ⋊ C22×C32 |
| Hall | C32×C13⋊C3 ⋊ C22 |
| Sylow | C13 ⋊ C2×C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊(D13⋊C3) |
| commutator, cosocle, hypocenter | C3×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2×C3 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 192);