Finite Group DatabasebetaFinite Group Databasebeta| order | 32604 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D33⋊D19 |
| unambiguous semidirect product | D33⋊(C13×D19) |
| unambiguous semidirect product | D57⋊(C13×D11) |
| unambiguous semidirect product | D209⋊(D3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D33⋊D19 |
| commutator, cosocle, hypocenter | C3×C11×C19 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C13×C19 | C22 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 ◁ C13 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8151 |
2379 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32604, 152);