Finite Group DatabasebetaFinite Group Databasebeta| order | 27132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | D7×C19×D51 |
| unambiguous semidirect product | (C3×D7)⋊(C19×D17) |
| unambiguous semidirect product | (D7×C17)⋊(D3×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D7×D51 |
| commutator, cosocle, hypocenter | C3×C7×C17 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17×C19 | C22 |
| LCS | G ▷ C3×C7×C17 | |
| UCS | C1 ◁ C19 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6783 |
2565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27132, 153);