Finite Group DatabasebetaFinite Group Databasebeta| order | 19550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×C5⋊D115 |
| unambiguous semidirect product | C5⋊(C17×D115) |
| unambiguous semidirect product | C23⋊(C17×C5⋊D5) |
| Fitting, socle, Hall | C52×C17×C23 ⋊ C2 |
| derived, Hall | C52×C23 ⋊ C2×C17 |
| Hall | C52×C17 ⋊ D23 |
| Hall | C17×C23 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C17×D23 |
| Sylow | C23 ⋊ C17×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C5⋊D115 |
| commutator, cosocle, hypocenter | C52×C23 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C23 | C2 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9775 |
4913 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19550, 12);