Finite Group DatabasebetaFinite Group Databasebeta| order | 12716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C11⋊#11923884 |
| Fitting, socle, derived, Hall | C11×C172 ⋊ C4 |
| Sylow | C172 ⋊ Dic11 |
| Sylow | C11 ⋊ #11923884 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C172 | C4 |
| prime radical, cosocle | C11×C17⋊D17 | C2 |
| LCS | G ▷ C11×C172 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,11,17^2|a^2=b,c^a=c^10,d^a=d^13,e^a=e^4,d^b=d^16,e^b=e^16806 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊#16812402, C3×C11⋊#11923884, C3⋊(C11⋊#11923884) |
| maximal normal subgroup of | C3×C11⋊#11923884 |
| maximal quotient of | C3×C11⋊#11923884, C3⋊(C11⋊#11923884) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12716, 27);