Finite Group DatabasebetaFinite Group Databasebeta| order | 33969 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C67⋊#92789 |
| Fitting, socle, derived, Hall | C132×C67 ⋊ C3 |
| Sylow | C132 ⋊ C67⋊C3 |
| Sylow | C67 ⋊ #92789 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C67 | C3 |
| LCS | G ▷ C132×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
Polycyclic presentation:
3,13^2,67|b^a=b^3,c^a=c^9,d^a=d^293777 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33969, 15);