Finite Group DatabasebetaFinite Group Databasebeta| order | 4444 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#87938 |
| Fitting, socle, derived, Hall | C11×C101 ⋊ C4 |
| Sylow | C101 ⋊ Dic11 |
| Sylow | C11 ⋊ #87938 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C101 | C4 |
| prime radical, cosocle | C11×D101 | C2 |
| LCS | G ▷ C11×C101 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 112 |
| transitive degree | μt(G) = 1111 |
Polycyclic presentation:
2^2,11,101|a^2=b,c^a=c^10,d^a=d^10,d^b=d^100289 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊#87938, C3⋊(C11⋊#87938), #36372473, … |
| maximal normal subgroup of | C3×C11⋊#87938, #36372473, #36372474, … |
| maximal quotient of | C3×C11⋊#87938, C3⋊(C11⋊#87938), C5×C11⋊#87938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4444, 7);