Finite Group DatabasebetaFinite Group Databasebeta| order | 27234 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C89 · Schur multiplier (H2) = C3 |
| direct product | C17×C3⋊D3×C89 |
| unambiguous semidirect product | C3⋊(D3×C17×C89) |
| Fitting, socle, Hall | C32×C17×C89 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C17×C89 |
| Hall | C32×C89 ⋊ C2×C17 |
| Hall | C32×C17 ⋊ C2×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C89 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C17×C89 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C89 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C17×C89 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13617 |
9078 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27234, 17);