Finite Group DatabasebetaFinite Group Databasebeta| order | 34188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#15690941 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #15690941 |
| commutator, hypocenter | C7×C37 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C37 | C3×C4 |
| prime radical | C11×#13095531 | C2 |
| cosocle | C7×D37 | C2×C3×C11 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2849 |
385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34188, 53);