Finite Group DatabasebetaFinite Group Databasebeta| order | 32620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#17987920 |
| Fitting, socle, Hall | C5×C7×C233 ⋊ C4 |
| derived, Hall | C5×C233 ⋊ C4×C7 |
| Hall | C7×C233 ⋊ Dic5 |
| Sylow | C233 ⋊ C7×Dic5 |
| Hall | C5×C7 ⋊ #11745400 |
| Sylow | C5 ⋊ C7×#11745400 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #17987920 |
| commutator, hypocenter | C5×C233 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C233 | C4 |
| prime radical | C5×C7×D233 | C2 |
| cosocle | C5×D233 | C2×C7 |
| LCS | G ▷ C5×C233 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8155 |
2086 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32620, 21);