Finite Group DatabasebetaFinite Group Databasebeta| order | 22382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C19⋊D589 |
| unambiguous semidirect product | C31⋊(C19⋊D19) |
| Fitting, socle, derived, Hall | C192×C31 ⋊ C2 |
| Sylow | C192 ⋊ D31 |
| Sylow | C31 ⋊ C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C192×C31 | C2 |
| LCS | G ▷ C192×C31 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11191 |
Polycyclic presentation:
2,19^2,31|b^a=b^18,c^a=c^18,d^a=d^305597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22382, 10);