Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D5×#11762245 |
| unambiguous semidirect product | C5⋊(C2×C3×#11762245) |
| Fitting, socle | C3×C5×C192 ⋊ C2×C3 |
| derived, Hall | C5×C192 ⋊ C2×C32 |
| Hall | C3×C5×#11762245 ⋊ C2 |
| Hall | D5×C192 ⋊ C32 |
| Sylow | C192 ⋊ C32×D5 |
| Sylow | C5 ⋊ C2×C3×#11762245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×#11762245 |
| commutator, cosocle, hypocenter | C5×C192 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C192 | C2×C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 ◁ C3 | |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5415 |
1476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 173);