Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C31⋊#11744707 |
| Fitting, socle, derived, Hall | C32×C52×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ #157 |
| Hall | C32×C31 ⋊ #1043 |
| Hall | C32×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ #11744707 |
| Sylow | C52 ⋊ C31⋊#157 |
| Sylow | C32 ⋊ C31⋊#1043 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52×C31 | C4 |
| prime radical, cosocle | C31×C3⋊(C3⋊(C5⋊D5)) | C2 |
| LCS | G ▷ C32×C52×C31 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5^2,31|a^2=b,c^a=cd,d^a=cd^2,e^a=e^2,f^a=f^2,g^a=g^30,c^b=c^2,d^b=d^2,e^b=e^4,f^b=f^41770 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 628);