Finite Group DatabasebetaFinite Group Databasebeta| order | 33852 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#22554953 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C7×C13×C31 | C3 |
| LCS | G ▷ C22×C7×C13×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11284 |
Polycyclic presentation:
3,2^2,7,13,31|b^a=c,c^a=bc,d^a=d^2,e^a=e^3,f^a=f^253764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33852, 409);