Finite Group DatabasebetaFinite Group Databasebeta| order | 32620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic1165 |
| derived, Hall | C5×C233 ⋊ C4×C7 |
| Hall | C5×C7×C233 ⋊ C4 |
| Hall | C7×C233 ⋊ Dic5 |
| Sylow | C233 ⋊ C7×Dic5 |
| Hall | C5×C7 ⋊ Dic233 |
| Sylow | C5 ⋊ C7×Dic233 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D1165 |
| commutator, hypocenter | C5×C233 | C4×C7 |
| Frattini | C2 | C7×D1165 |
| Fitting, socle, prime radical | C2×C5×C7×C233 | C2 |
| cosocle | C2×C5×C233 | C2×C7 |
| LCS | G ▷ C5×C233 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32620 |
8176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32620, 6);