Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C5 |
| direct product | C17×D19×C5⋊D5 |
| unambiguous semidirect product | (C5×D19)⋊(D5×C17) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C22 |
| derived, Hall | C52×C19 ⋊ C22×C17 |
| Hall | C52×C17 ⋊ C2×D19 |
| Hall | C17×C19 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×C17×D19 |
| Sylow | C19 ⋊ C2×C17×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D19×C5⋊D5 |
| commutator, cosocle, hypocenter | C52×C19 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C22 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C17 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
2618 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 86);