Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C5 |
| direct product | C19×#13133334 |
| derived, Hall | C52×C17 ⋊ C4×C19 |
| Hall | C52×C17×C19 ⋊ C4 |
| Hall | C52×C19 ⋊ Dic17 |
| Hall | C17×C19 ⋊ #1039 |
| Sylow | C52 ⋊ C19×Dic17 |
| Sylow | C17 ⋊ C19×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | C5⋊D85 |
| commutator, hypocenter | C52×C17 | C4×C19 |
| Frattini | C2 | C19×C5⋊D85 |
| Fitting, socle, prime radical | C2×C52×C17×C19 | C2 |
| cosocle | C2×C52×C17 | C2×C19 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C2×C19 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32300 |
8132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 38);