Finite Group DatabasebetaFinite Group Databasebeta| order | 33540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | D3×C13×D215 |
| unambiguous semidirect product | (C5×D3)⋊(C13×D43) |
| unambiguous semidirect product | (D3×C43)⋊(D5×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D3×D215 |
| commutator, cosocle, hypocenter | C3×C5×C43 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C43 | C22 |
| LCS | G ▷ C3×C5×C43 | |
| UCS | C1 ◁ C13 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8385 |
4251 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33540, 199);