Finite Group DatabasebetaFinite Group Databasebeta| order | 22382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C19 |
| direct product | C31×C19⋊D19 |
| unambiguous semidirect product | C19⋊(C31×D19) |
| Fitting, socle, Hall | C192×C31 ⋊ C2 |
| derived, Sylow | C192 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C19⋊D19 |
| commutator, cosocle, hypocenter | C192 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C192×C31 | C2 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C31 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11191 |
5642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22382, 9);