Finite Group DatabasebetaFinite Group Databasebeta| order | 22116 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C19⋊#87604 |
| Fitting, socle, Hall | C3×C19×C97 ⋊ C4 |
| derived, Hall | C19×C97 ⋊ C3×C4 |
| Hall | C3×C97 ⋊ Dic19 |
| Sylow | C97 ⋊ C3×Dic19 |
| Hall | C3×C19 ⋊ #87604 |
| Sylow | C19 ⋊ C3×#87604 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊#87604 |
| commutator, hypocenter | C19×C97 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C97 | C4 |
| prime radical | C3×C19×D97 | C2 |
| cosocle | C19×D97 | C2×C3 |
| LCS | G ▷ C19×C97 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5529 |
1434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22116, 51);