Finite Group DatabasebetaFinite Group Databasebeta| order | 32604 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#13093361⋊C2 |
| unambiguous semidirect product | #13093361⋊(C2×C11) |
| unambiguous semidirect product | #13093365⋊(C2×C11) |
| unambiguous semidirect product | #13093367⋊(C2×C11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #13093361⋊C2 |
| commutator, cosocle, hypocenter | C13×C19 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C19 | C22×C3 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C11 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2717 |
440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32604, 57);