Finite Group DatabasebetaFinite Group Databasebeta| order | 22010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D31⋊C5 |
| unambiguous semidirect product | D31⋊(C5×C71) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C2×C71) |
| Fitting, socle, Hall | C31×C71 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C2×C5×C71 |
| Hall | C71×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D31×C71 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×C71 |
| Hall | D31 ⋊ C5×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C71 |
| Frattini | C1 | G |
| Fitting, socle | C31×C71 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2201 |
923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22010, 22);