Finite Group DatabasebetaFinite Group Databasebeta| order | 22570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D61⋊C5 |
| unambiguous semidirect product | D61⋊(C5×C37) |
| unambiguous semidirect product | (C61⋊C5)⋊(C2×C37) |
| unambiguous semidirect product | (C37×D61)⋊C5 |
| Fitting, socle, Hall | C37×C61 ⋊ C2×C5 |
| derived, Sylow | C61 ⋊ C2×C5×C37 |
| Hall | C37×C61⋊C5 ⋊ C2 |
| Hall | C37×D61 ⋊ C5 |
| Hall | C61⋊C5 ⋊ C2×C37 |
| Hall | D61 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C2×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C61 | C2×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2257 |
592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22570, 10);