Finite Group DatabasebetaFinite Group Databasebeta| order | 33753 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11251⋊C3 |
| Fitting, socle, derived, Sylow | C11251 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11251 | C3 |
| LCS | G ▷ C11251 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11251 |
Polycyclic presentation:
3,11251|b^a=b^10763753 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33753, 1);