Finite Group DatabasebetaFinite Group Databasebeta| order | 22002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C19×D193 |
| Fitting, socle, Hall | C3×C19×C193 ⋊ C2 |
| derived, Sylow | C193 ⋊ C2×C3×C19 |
| Hall | C19×C193 ⋊ C2×C3 |
| Hall | C3×C193 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | D193 |
| commutator, cosocle, hypocenter | C193 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C193 | C2 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C3×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11001 |
5586 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22002, 6);