Finite Group DatabasebetaFinite Group Databasebeta| order | 22010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D355 |
| unambiguous semidirect product | C5⋊(C31×D71) |
| unambiguous semidirect product | C71⋊(D5×C31) |
| Fitting, socle, Hall | C5×C31×C71 ⋊ C2 |
| derived, Hall | C5×C71 ⋊ C2×C31 |
| Hall | C31×C71 ⋊ D5 |
| Hall | C5×C31 ⋊ D71 |
| Sylow | C71 ⋊ D5×C31 |
| Sylow | C5 ⋊ C31×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D355 |
| commutator, cosocle, hypocenter | C5×C71 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C71 | C2 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11005 |
5549 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22010, 12);