Finite Group DatabasebetaFinite Group Databasebeta| order | 29172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D221⋊D33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C13×C17 | C22 |
| LCS | G ▷ C3×C11×C13×C17 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7293 |
Polycyclic presentation:
2^2,3,11,13,17|e^a=e^12,f^a=f^16,c^b=c^2,d^b=d^10,e^b=e^121872 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29172, 94);