Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C5 |
| unambiguous semidirect product | (C22⋊(C52⋊C3))⋊(C31⋊C3) |
| unambiguous semidirect product | (C22⋊(C31⋊C3))⋊(C52⋊C3) |
| unambiguous semidirect product | (C52⋊(C31⋊C3))⋊A4 |
| Fitting, socle, derived, Hall | C22×C52×C31 ⋊ C32 |
| Hall | C52×C31 ⋊ C3×A4 |
| Hall | C22×C31 ⋊ C3×C52⋊C3 |
| Hall | C22×C52 ⋊ C3×C31⋊C3 |
| Sylow | C31 ⋊ A4×C52⋊C3 |
| Sylow | C52 ⋊ A4×C31⋊C3 |
| Sylow | C22 ⋊ C52⋊C3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C52×C31 | C32 |
| LCS | G ▷ C22×C52×C31 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,2^2,5^2,31|e^a=e^4f^2,f^a=e^2,g^a=g^5,c^b=cd,d^b=c,e^b=e^4f^2,f^b=e^2404 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 584);