Finite Group DatabasebetaFinite Group Databasebeta| order | 32220 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C179 · Schur multiplier (H2) = C2 |
| derived, Sylow | C22 ⋊ C5×C9×C179 |
| Hall | C22×C5×C179 ⋊ C9 |
| Hall | C22×C179 ⋊ C5×C9 |
| Hall | C22×C5 ⋊ C9×C179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C179 | A4 |
| commutator, hypocenter | C22 | C5×C9×C179 |
| Frattini | C3 | C5×A4×C179 |
| Fitting, socle, prime radical | C22×C3×C5×C179 | C3 |
| cosocle | C22×C3 | C3×C5×C179 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C5×C179 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16110 |
10740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32220, 21);