Finite Group DatabasebetaFinite Group Databasebeta| order | 34164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#22555436 |
| derived, Hall | C13×C73 ⋊ C22×C9 |
| Hall | C22×C13×C73 ⋊ C9 |
| Hall | C22×C73 ⋊ C13⋊C9 |
| Sylow | C73 ⋊ C22×C13⋊C9 |
| Hall | C22×C13 ⋊ #10620321 |
| Sylow | C13 ⋊ C22×#10620321 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #15667865 |
| commutator, hypocenter | C13×C73 | C22×C9 |
| Frattini | C3 | C22×#15667865 |
| Fitting, socle, prime radical | C22×C3×C13×C73 | C3 |
| cosocle | C3×C13×C73 | C22×C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 ◁ C22×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34164 |
3828 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34164, 91);