Finite Group DatabasebetaFinite Group Databasebeta| order | 36723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C12241⋊C3 |
| Fitting, socle, derived, Sylow | C12241 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12241 | C3 |
| LCS | G ▷ C12241 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12241 |
Polycyclic presentation:
3,12241|b^a=b^29334083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36723, 1);