Finite Group DatabasebetaFinite Group Databasebeta| order | 34188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D77⋊D111 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C11×C37 | C22 |
| LCS | G ▷ C3×C7×C11×C37 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8547 |
Polycyclic presentation:
2^2,3,7,11,37|c^a=c^2,e^a=e^10,f^a=f^36,d^b=d^6,e^b=e^102235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34188, 162);