Finite Group DatabasebetaFinite Group Databasebeta| order | 9724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#11725131 |
| Fitting, socle, derived, Hall | C11×C13×C17 ⋊ C4 |
| Hall | C13×C17 ⋊ Dic11 |
| Hall | C11×C17 ⋊ #261 |
| Hall | C11×C13 ⋊ #595 |
| Sylow | C17 ⋊ C11⋊#261 |
| Sylow | C13 ⋊ C11⋊#595 |
| Sylow | C11 ⋊ #11725131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C13×C17 | C4 |
| prime radical, cosocle | C11×D221 | C2 |
| LCS | G ▷ C11×C13×C17 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,11,13,17|a^2=b,c^a=c^10,d^a=d^5,e^a=e^4,d^b=d^12,e^b=e^16619 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊(#11725131⋊C3), C3×C11⋊#11725131, C3⋊(C11⋊#11725131) |
| maximal normal subgroup of | C11⋊(#11725131⋊C3), C3×C11⋊#11725131 |
| maximal quotient of | C3×C11⋊#11725131, C3⋊(C11⋊#11725131) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9724, 21);