Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D27 |
| unambiguous semidirect product | C27⋊(C22×C13) |
| unambiguous semidirect product | (C2×C27)⋊(C2×C13) |
| Fitting | C2×C13×C27 ⋊ C2 |
| derived, Sylow | C27 ⋊ C22×C13 |
| Hall | C13×C27 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D27 |
| commutator, cosocle, hypocenter | C27 | C22×C13 |
| Frattini | C9 | C2×D3×C13 |
| Fitting | C2×C13×C27 | C2 |
| socle | C2×C3×C13 | D9 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C2×C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 702 |
390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 16);