Finite Group DatabasebetaFinite Group Databasebeta| order | 22570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C37⋊(D61⋊C5) |
| unambiguous semidirect product | (C61⋊C5)⋊D37 |
| unambiguous semidirect product | D2257⋊C5 |
| Fitting, socle, derived, Hall | C37×C61 ⋊ C2×C5 |
| Hall | C37×C61⋊C5 ⋊ C2 |
| Hall | D2257 ⋊ C5 |
| Hall | C61⋊C5 ⋊ D37 |
| Sylow | C61 ⋊ C5×D37 |
| Sylow | C37 ⋊ D61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C61 | C2×C5 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2257 |
Polycyclic presentation:
2,5,37,61|c^a=c^36,d^a=d^60,d^b=d^9322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22570, 12);