Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D5×D15×C31⋊C3 |
| unambiguous semidirect product | (C3×D5)⋊(D5×C31⋊C3) |
| unambiguous semidirect product | (C5×D5)⋊(D3×C31⋊C3) |
| unambiguous semidirect product | (D5×D15×C31)⋊C3 |
| Fitting, socle, derived | C3×C52×C31 ⋊ C22×C3 |
| Hall | C3×C52×C31⋊C3 ⋊ C22 |
| Hall | C52×C31 ⋊ C2×C3×D3 |
| Hall | C3×C31⋊C3 ⋊ D52 |
| Sylow | C31 ⋊ C3×D5×D15 |
| Sylow | C52 ⋊ C2×D3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C31 | C22×C3 |
| LCS | G ▷ C3×C52×C31 | |
| UCS | C1 | |
212 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 556);