Finite Group DatabasebetaFinite Group Databasebeta| order | 3916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C4×C89⋊C11 |
| unambiguous semidirect product | (C4×C89)⋊C11 |
| Fitting, Hall | C4×C89 ⋊ C11 |
| derived, Sylow | C89 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C89⋊C11 |
| commutator, hypocenter | C89 | C4×C11 |
| Frattini | C2 | C2×C89⋊C11 |
| Fitting | C4×C89 | C11 |
| socle, cosocle | C2×C89 | C2×C11 |
| prime radical | C2×C89⋊C11 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 356 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C89⋊C11, Dic3×C89⋊C11, C4×C5×C89⋊C11, … |
| maximal normal subgroup of | C3×C4×C89⋊C11, C4×C5×C89⋊C11, C4×C7×C89⋊C11 |
| maximal quotient of | C3×C4×C89⋊C11, Dic3×C89⋊C11, C4×C5×C89⋊C11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3916, 3);