Finite Group DatabasebetaFinite Group Databasebeta| order | 19620 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#14546129 |
| Fitting, socle, Hall | C32×C5×C109 ⋊ C4 |
| derived, Hall | C5×C109 ⋊ C32×C4 |
| Hall | C32×C109 ⋊ Dic5 |
| Sylow | C109 ⋊ C32×Dic5 |
| Hall | C32×C5 ⋊ #89137 |
| Sylow | C5 ⋊ C32×#89137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #14546129 |
| commutator, hypocenter | C5×C109 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C109 | C4 |
| prime radical | C32×C5×D109 | C2 |
| cosocle | C5×D109 | C2×C32 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4905 |
1287 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19620, 122);