Finite Group DatabasebetaFinite Group Databasebeta| order | 19744 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D617 |
| unambiguous semidirect product | C617⋊C25 |
| unambiguous semidirect product | (C2×C617)⋊C24 |
| Fitting, socle | C24×C617 ⋊ C2 |
| derived, Sylow | C617 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D617 |
| commutator, cosocle, hypocenter | C617 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C617 | C2 |
| LCS | G ▷ C617 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9872 |
4960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19744, 195);