Finite Group DatabasebetaFinite Group Databasebeta| order | 3916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic89⋊C11 |
| derived, Sylow | C89 ⋊ C4×C11 |
| Hall | C89⋊C11 ⋊ C4 |
| Hall | Dic89 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D89⋊C11 |
| commutator, hypocenter | C89 | C4×C11 |
| Fitting, socle, cosocle | C2×C89 | C2×C11 |
| prime radical | C2×C89⋊C11 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 356 |
Polycyclic presentation:
2,11,89,2|a^2=d,c^a=c^88,c^b=c^6452 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic89⋊C11, C3⋊(Dic89⋊C11), C5×Dic89⋊C11, … |
| maximal normal subgroup of | C3×Dic89⋊C11, C5×Dic89⋊C11, C7×Dic89⋊C11 |
| maximal quotient of | C3×Dic89⋊C11, C3⋊(Dic89⋊C11), C5×Dic89⋊C11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3916, 2);