Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×ΓL(1,𝔽16)×C31⋊C3 |
| unambiguous semidirect product | C3⋊(C5×AGL(1,𝔽5)×C31⋊C3) |
| unambiguous semidirect product | (C5×C31×ΓL(1,𝔽16))⋊C3 |
| Fitting, socle | C3×C52×C31 ⋊ C3×C4 |
| derived | C3×C5×C31 ⋊ C3×C4×C5 |
| Hall | C3×C52×C31⋊C3 ⋊ C4 |
| Hall | C52×C31 ⋊ C3×Dic3 |
| Hall | C3×C31⋊C3 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C31 ⋊ C3×C5×ΓL(1,𝔽16) |
| Sylow | C52 ⋊ Dic3×C31⋊C3 |
124 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
585 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 550);