Finite Group DatabasebetaFinite Group Databasebeta| order | 27522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D4587 |
| unambiguous semidirect product | C11⋊(C3⋊D417) |
| unambiguous semidirect product | C139⋊(C3⋊D33) |
| Fitting, socle, derived, Hall | C32×C11×C139 ⋊ C2 |
| Hall | C11×C139 ⋊ C3⋊D3 |
| Hall | C32×C139 ⋊ D11 |
| Sylow | C139 ⋊ C3⋊D33 |
| Hall | C32×C11 ⋊ D139 |
| Sylow | C11 ⋊ C3⋊D417 |
| Sylow | C32 ⋊ D1529 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C11×C139 | C2 |
| LCS | G ▷ C32×C11×C139 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13761 |
Polycyclic presentation:
2,3^2,11,139|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^1386882 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27522, 32);