Finite Group DatabasebetaFinite Group Databasebeta| order | 19356 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#20264563 |
| Fitting, socle, Hall | C3×C1613 ⋊ C4 |
| derived, Sylow | C1613 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20264563 |
| commutator, hypocenter | C1613 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1613 | C4 |
| prime radical | C3×D1613 | C2 |
| cosocle | D1613 | C2×C3 |
| LCS | G ▷ C1613 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4839 |
1221 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19356, 6);