Finite Group DatabasebetaFinite Group Databasebeta| order | 22082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D181 |
| unambiguous semidirect product | C181⋊(C2×C61) |
| Fitting, socle, Hall | C61×C181 ⋊ C2 |
| derived, Sylow | C181 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D181 |
| commutator, cosocle, hypocenter | C181 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C61×C181 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C61 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11041 |
5612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22082, 2);