Finite Group DatabasebetaFinite Group Databasebeta| order | 19788 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1649⋊C3 |
| derived, Hall | C17×C97 ⋊ C3×C4 |
| Hall | Dic1649 ⋊ C3 |
| Hall | C17×C97⋊C3 ⋊ C4 |
| Hall | C97⋊C3 ⋊ Dic17 |
| Sylow | C97 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ Dic97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊(D97⋊C3) |
| commutator, hypocenter | C17×C97 | C3×C4 |
| Fitting, socle, cosocle | C2×C17×C97 | C2×C3 |
| prime radical | C2×C17×C97⋊C3 | C2 |
| LCS | G ▷ C17×C97 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6596 |
Polycyclic presentation:
2,3,17,97,2|a^2=e,c^a=c^16,d^a=d^96,d^b=d^35604 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19788, 12);