Finite Group DatabasebetaFinite Group Databasebeta| order | 19788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C17⋊(D97⋊C3) |
| unambiguous semidirect product | (C2×C17)⋊(D97⋊C3) |
| unambiguous semidirect product | (C2×C97⋊C3)⋊D17 |
| unambiguous semidirect product | (C2×D1649)⋊C3 |
| Fitting, socle | C2×C17×C97 ⋊ C2×C3 |
| derived, Hall | C17×C97 ⋊ C22×C3 |
| Hall | C2×D1649 ⋊ C3 |
| Hall | C17×C97⋊C3 ⋊ C22 |
| Hall | C97⋊C3 ⋊ C2×D17 |
| Sylow | C97 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C2×D97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C17⋊(D97⋊C3) |
| commutator, cosocle, hypocenter | C17×C97 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C97 | C2×C3 |
| LCS | G ▷ C17×C97 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3298 |
604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19788, 22);