Finite Group DatabasebetaFinite Group Databasebeta| order | 22010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D155 |
| unambiguous semidirect product | C5⋊(D31×C71) |
| unambiguous semidirect product | C31⋊(D5×C71) |
| Fitting, socle, Hall | C5×C31×C71 ⋊ C2 |
| derived, Hall | C5×C31 ⋊ C2×C71 |
| Hall | C31×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ D31 |
| Sylow | C31 ⋊ D5×C71 |
| Sylow | C5 ⋊ D31×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D155 |
| commutator, cosocle, hypocenter | C5×C31 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C71 | C2 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11005 |
5609 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22010, 13);