Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(C31⋊#1042) |
| unambiguous semidirect product | C3⋊(C3×C31⋊#1042) |
| Fitting, socle, Hall | C32×C52×C31 ⋊ C4 |
| derived | C3×C52×C31 ⋊ C3×C4 |
| Hall | C52×C31 ⋊ C3×Dic3 |
| Hall | C32×C31 ⋊ #1042 |
| Hall | C32×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ C3×C3⋊#1042 |
| Sylow | C52 ⋊ C3×Dic93 |
| Sylow | C32 ⋊ C31⋊#1042 |
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2799 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 653);