Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C31 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | A4×C31×C52⋊C3 |
| unambiguous semidirect product | (C22×C52⋊C3)⋊(C3×C31) |
| unambiguous semidirect product | (C52×A4)⋊(C3×C31) |
| unambiguous semidirect product | (C22⋊(C52⋊C3))⋊(C3×C31) |
| Fitting, socle, Hall | C22×C52×C31 ⋊ C32 |
| derived, Hall | C22×C52 ⋊ C32×C31 |
| Hall | C52×C31 ⋊ C3×A4 |
| Hall | C22×C31 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×A4×C31 |
| Sylow | C22 ⋊ C3×C31×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | A4×C52⋊C3 |
| commutator, cosocle, hypocenter | C22×C52 | C32×C31 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C31 | C32 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C31 | |
76 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 581);