Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C32⋊(C22⋊(C13⋊C3)) |
| Fitting | C22×C32×C13 ⋊ C3 |
| Hall | C22×C13 ⋊ H(3,𝔽3) |
| Sylow | C13 ⋊ C22⋊H(3,𝔽3) |
| Sylow | C22 ⋊ C32⋊(C13⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C22⋊(C13⋊C3) |
| commutator, socle, cosocle | C22×C3×C13 | C32 |
| Fitting | C22×C32×C13 | C3 |
| hypercenter | C32 | C22⋊(C13⋊C3) |
| hypocenter | C22×C13 | H(3,𝔽3) |
| LCS | G ▷ C22×C3×C13 ▷ C22×C13 | |
| UCS | C1 ◁ C3 ◁ C32 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 234 |
Polycyclic presentation:
3^3,2^2,13|b^a=bc,d^a=de,e^a=d,f^a=f^3164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 141);