Finite Group DatabasebetaFinite Group Databasebeta| order | 22126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23×C37 · Schur multiplier (H2) = C1 |
| direct product | C23×D13×C37 |
| unambiguous semidirect product | C13⋊(C2×C23×C37) |
| Fitting, socle, Hall | C13×C23×C37 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C23×C37 |
| Hall | C13×C37 ⋊ C2×C23 |
| Hall | C13×C23 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C37 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C23×C37 |
| Frattini | C1 | G |
| Fitting, socle | C13×C23×C37 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11063 |
6808 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22126, 5);