Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of AGL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽27) |
| unambiguous semidirect product | (C2×C3⋊(C3⋊D3))⋊C13 |
| unambiguous semidirect product | (C33⋊C13)⋊C22 |
| unambiguous semidirect product | (C2×C33⋊C13)⋊C2 |
| Fitting, socle | C2×C33 ⋊ C2×C13 |
| derived, Sylow | C33 ⋊ C22×C13 |
| Hall | C33⋊C13 ⋊ C22 |
| Hall | C2×C3⋊(C3⋊D3) ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽27) |
| commutator, cosocle, hypocenter | C33 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | C2×C13 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13×AGL(1,𝔽27) |
| maximal normal subgroup of | C2×C13×AGL(1,𝔽27) |
| maximal quotient of | C2×C13×AGL(1,𝔽27) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 176);