Finite Group DatabasebetaFinite Group Databasebeta| order | 22422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C101⋊(D37⋊C3) |
| unambiguous semidirect product | (C37⋊C3)⋊D101 |
| unambiguous semidirect product | D3737⋊C3 |
| Fitting, socle, derived, Hall | C37×C101 ⋊ C2×C3 |
| Hall | C101×C37⋊C3 ⋊ C2 |
| Hall | D3737 ⋊ C3 |
| Hall | C37⋊C3 ⋊ D101 |
| Sylow | C101 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ C3×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C101 | C2×C3 |
| LCS | G ▷ C37×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3737 |
Polycyclic presentation:
2,3,37,101|c^a=c^36,d^a=d^100,c^b=c^26762 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22422, 12);