Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D19×D85 |
| unambiguous semidirect product | (C5×D19)⋊(C5×D17) |
| unambiguous semidirect product | (C17×D19)⋊(C5×D5) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C22 |
| derived | C5×C17×C19 ⋊ C22×C5 |
| Hall | C52×C19 ⋊ C2×D17 |
| Hall | C52×C17 ⋊ C2×D19 |
| Hall | C17×C19 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ D17×D19 |
| Sylow | C19 ⋊ C2×C5×D85 |
| Sylow | C17 ⋊ C5×D5×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D19×D85 |
| commutator, cosocle, hypocenter | C5×C17×C19 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C22 |
| LCS | G ▷ C5×C17×C19 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3230 |
2420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 55);