Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic323 |
| unambiguous semidirect product | C19⋊(C25×Dic17) |
| derived, Hall | C17×C19 ⋊ C4×C25 |
| Hall | C17×C19×C25 ⋊ C4 |
| Hall | C19×C25 ⋊ Dic17 |
| Hall | C17×C25 ⋊ Dic19 |
| Sylow | C19 ⋊ C25×Dic17 |
| Sylow | C17 ⋊ C25×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D323 |
| commutator, hypocenter | C17×C19 | C4×C25 |
| Frattini | C2×C5 | C5×D323 |
| Fitting | C2×C17×C19×C25 | C2 |
| socle, prime radical, cosocle | C2×C5×C17×C19 | C2×C5 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 ◁ C2×C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32300 |
8150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 4);