Finite Group DatabasebetaFinite Group Databasebeta| order | 22220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×(C11⋊C5)⋊D101 |
| unambiguous semidirect product | (C2×C11⋊C5)⋊D101 |
| Fitting, socle | C2×C11×C101 ⋊ C2×C5 |
| derived, Hall | C11×C101 ⋊ C22×C5 |
| Hall | C11⋊C5×C101 ⋊ C22 |
| Hall | C2×D1111 ⋊ C5 |
| Sylow | C101 ⋊ C2×AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ C2×D101 |
| Sylow | C11 ⋊ C2×C5×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C11⋊C5)⋊D101 |
| commutator, cosocle, hypocenter | C11×C101 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C101 | C2×C5 |
| LCS | G ▷ C11×C101 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2222 |
722 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22220, 62);