Finite Group DatabasebetaFinite Group Databasebeta| order | 27234 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D4539 |
| unambiguous semidirect product | C17⋊(C3⋊D267) |
| unambiguous semidirect product | C89⋊(C3⋊D51) |
| Fitting, socle, derived, Hall | C32×C17×C89 ⋊ C2 |
| Hall | C17×C89 ⋊ C3⋊D3 |
| Hall | C32×C89 ⋊ D17 |
| Hall | C32×C17 ⋊ D89 |
| Sylow | C89 ⋊ C3⋊D51 |
| Sylow | C17 ⋊ C3⋊D267 |
| Sylow | C32 ⋊ D1513 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C17×C89 | C2 |
| LCS | G ▷ C32×C17×C89 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13617 |
Polycyclic presentation:
2,3^2,17,89|b^a=b^2,c^a=c^2,d^a=d^16,e^a=e^886810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27234, 20);