Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic2325 |
| unambiguous semidirect product | C31⋊(C3⋊Dic75) |
| derived, Hall | C32×C25×C31 ⋊ C4 |
| Hall | C25×C31 ⋊ C3⋊Dic3 |
| Hall | C32×C31 ⋊ Dic25 |
| Hall | C32×C25 ⋊ Dic31 |
| Sylow | C31 ⋊ C3⋊Dic75 |
| Sylow | C25 ⋊ C3⋊Dic93 |
| Sylow | C32 ⋊ Dic775 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D2325 |
| commutator, hypocenter | C32×C25×C31 | C4 |
| Frattini | C2×C5 | C3⋊D465 |
| Fitting, cosocle | C2×C32×C25×C31 | C2 |
| socle, prime radical | C2×C32×C5×C31 | D5 |
| LCS | G ▷ C32×C25×C31 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,31,2,5|a^2=f,d^5=g^4,b^a=b^2,c^a=c^2,d^a=d^4g,e^a=e^30,g^a=g^46978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 85);