Finite Group DatabasebetaFinite Group Databasebeta| order | 33644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic647 |
| unambiguous semidirect product | C647⋊(C4×C13) |
| derived, Sylow | C647 ⋊ C4×C13 |
| Hall | C13×C647 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D647 |
| commutator, hypocenter | C647 | C4×C13 |
| Frattini | C2 | C13×D647 |
| Fitting, socle, prime radical | C2×C13×C647 | C2 |
| cosocle | C2×C647 | C2×C13 |
| LCS | G ▷ C647 | |
| UCS | C1 ◁ C2×C13 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33644 |
8450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33644, 3);