Finite Group DatabasebetaFinite Group Databasebeta| order | 36652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D187⋊D49 |
| unambiguous semidirect product | D539⋊D17 |
| unambiguous semidirect product | D833⋊D11 |
| Fitting, derived, Hall | C11×C17×C49 ⋊ C22 |
| Hall | C17×C49 ⋊ C2×D11 |
| Hall | C11×C49 ⋊ C2×D17 |
| Hall | C11×C17 ⋊ C2×D49 |
| Sylow | C49 ⋊ D11×D17 |
| Sylow | C17 ⋊ D11×D49 |
| Sylow | C11 ⋊ D17×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C17×C49 | C22 |
| Frattini | C7 | D77⋊D17 |
| socle | C7×C11×C17 | C2×D7 |
| LCS | G ▷ C11×C17×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9163 |
Polycyclic presentation:
2^2,7,11,17,7|c^7=f^6,d^a=d^10,e^a=e^16,c^b=c^6f,d^b=d^10,f^b=f^62350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36652, 20);