Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C3⋊(D31⋊(C52⋊C3)) |
| unambiguous semidirect product | (C2×C3)⋊(D31⋊(C52⋊C3)) |
| unambiguous semidirect product | (C2×D93)⋊(C52⋊C3) |
| Fitting, socle | C2×C3×C52×C31 ⋊ C2×C3 |
| derived | C3×C52×C31 ⋊ C22×C3 |
| Hall | C3×C52⋊(C31⋊C3) ⋊ C22 |
| Hall | C52×C31 ⋊ C2×C3×D3 |
| Sylow | C31 ⋊ C2×D3×C52⋊C3 |
| Sylow | C52 ⋊ C2×C3⋊(D31⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(D31⋊(C52⋊C3)) |
| commutator, cosocle, hypocenter | C3×C52×C31 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C31 | C2×C3 |
| LCS | G ▷ C3×C52×C31 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
816 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 601);