Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C4×#18012457 |
| Fitting, Hall | C4×C312 ⋊ C5 |
| derived, Sylow | C312 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #18012457 |
| commutator, hypocenter | C312 | C4×C5 |
| Frattini | C2 | C2×#18012457 |
| Fitting | C4×C312 | C5 |
| socle, cosocle | C2×C312 | C2×C5 |
| prime radical | C2×#18012457 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C4 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 620 |
788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 30);