Finite Group DatabasebetaFinite Group Databasebeta| order | 10076 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#11745021 |
| Fitting, socle, derived, Hall | C11×C229 ⋊ C4 |
| Sylow | C229 ⋊ Dic11 |
| Sylow | C11 ⋊ #11745021 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C229 | C4 |
| prime radical, cosocle | C11×D229 | C2 |
| LCS | G ▷ C11×C229 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,11,229|a^2=b,c^a=c^10,d^a=d^122,d^b=d^228641 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊(#11745021⋊C3), C3×C11⋊#11745021, C3⋊(C11⋊#11745021) |
| maximal normal subgroup of | C11⋊(#11745021⋊C3), C3×C11⋊#11745021 |
| maximal quotient of | C3×C11⋊#11745021, C3⋊(C11⋊#11745021) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10076, 7);