Finite Group DatabasebetaFinite Group Databasebeta| order | 29772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C827⋊#157 |
| Fitting, socle, derived, Hall | C32×C827 ⋊ C4 |
| Sylow | C827 ⋊ #157 |
| Sylow | C32 ⋊ Dic827 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C827 | C4 |
| prime radical, cosocle | C3⋊D3×C827 | C2 |
| LCS | G ▷ C32×C827 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4962 |
Polycyclic presentation:
2^2,3^2,827|a^2=b,c^a=cd,d^a=cd^2,e^a=e^826,c^b=c^2,d^b=d^22484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29772, 19);