Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C31⋊C3×#1042 |
| unambiguous semidirect product | (C31×#1042)⋊C32 |
| unambiguous semidirect product | (C3×C31×#1042)⋊C3 |
| Fitting, socle | C3×C52×C31 ⋊ C3×C4 |
| derived, Hall | C52×C31 ⋊ C32×C4 |
| Hall | C3×C52×C31⋊C3 ⋊ C4 |
| Hall | C31×#1042 ⋊ C32 |
| Sylow | C31 ⋊ C32×#1042 |
| Sylow | C52 ⋊ C3×C4×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C31⋊C3×#1042 |
| commutator, hypocenter | C52×C31 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C3×C4 |
| prime radical | C3×C5×D5×C31⋊C3 | C2 |
| cosocle | C5×D5×C31 | C2×C32 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C3 | |
156 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
507 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 504);