Finite Group DatabasebetaFinite Group Databasebeta| order | 23722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C409 · Schur multiplier (H2) = C1 |
| direct product | D29×C409 |
| unambiguous semidirect product | C29⋊(C2×C409) |
| Fitting, socle, Hall | C29×C409 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C409 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C409 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C409 |
| Frattini | C1 | G |
| Fitting, socle | C29×C409 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C409 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11861 |
6544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23722, 1);