Finite Group DatabasebetaFinite Group Databasebeta| order | 19744 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#19096928 |
| derived, Sylow | C617 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14578674 |
| commutator, hypocenter | C617 | C4×C8 |
| Frattini | C22 | C2×#14578674 |
| Fitting | C2×C4×C617 | C4 |
| socle, prime radical | C22×C617 | C2×C4 |
| cosocle | C2×Dic617 | C22 |
| LCS | G ▷ C617 | |
| UCS | C1 ◁ C2×C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19744 |
1264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19744, 199);