Finite Group DatabasebetaFinite Group Databasebeta| order | 27132 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic399 |
| unambiguous semidirect product | C3⋊(C17×Dic133) |
| unambiguous semidirect product | C7⋊(C17×Dic57) |
| unambiguous semidirect product | C19⋊(C17×Dic21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D399 |
| commutator, hypocenter | C3×C7×C19 | C4×C17 |
| Frattini | C2 | C17×D399 |
| Fitting, socle, prime radical | C2×C3×C7×C17×C19 | C2 |
| cosocle | C2×C3×C7×C19 | C2×C17 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 ◁ C2×C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27132 |
6834 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27132, 18);