Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊(C3⋊(C31⋊#1039)) |
| unambiguous semidirect product | C31⋊(C3⋊(C3⋊#1039)) |
| derived, Hall | C32×C52×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ C3⋊Dic3 |
| Hall | C32×C31 ⋊ #1039 |
| Hall | C32×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ C3⋊(C3⋊#1039) |
| Sylow | C52 ⋊ C3⋊Dic93 |
| Sylow | C32 ⋊ C31⋊#1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊(C5⋊D155)) |
| commutator, hypocenter | C32×C52×C31 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C52×C31 | C2 |
| LCS | G ▷ C32×C52×C31 | |
| UCS | C1 ◁ C2 | |
288 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5^2,31,2|a^2=g,b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^306978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 399);