Finite Group DatabasebetaFinite Group Databasebeta| order | 32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C173 · Schur multiplier (H2) = C1 |
| direct product | C5×D19×C173 |
| unambiguous semidirect product | C19⋊(C2×C5×C173) |
| Fitting, socle, Hall | C5×C19×C173 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C5×C173 |
| Hall | C19×C173 ⋊ C2×C5 |
| Hall | C5×C19 ⋊ C2×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C173 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C5×C173 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C173 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C173 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16435 |
9515 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32870, 3);