Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×C19⋊#1044 |
| unambiguous semidirect product | C19⋊(C17×#1044) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C4 |
| derived, Hall | C52×C19 ⋊ C4×C17 |
| Hall | C52×C17 ⋊ Dic19 |
| Hall | C17×C19 ⋊ #1044 |
| Sylow | C52 ⋊ C17×Dic19 |
| Sylow | C19 ⋊ C17×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C19⋊#1044 |
| commutator, hypocenter | C52×C19 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C4 |
| prime radical | C17×C19×C5⋊D5 | C2 |
| cosocle | C19×C5⋊D5 | C2×C17 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3230 |
2312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 103);