Finite Group DatabasebetaFinite Group Databasebeta| order | 12628 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C7⋊#4223 |
| unambiguous semidirect product | C7⋊(C11×#4223) |
| Fitting, socle, Hall | C7×C11×C41 ⋊ C4 |
| derived, Hall | C7×C41 ⋊ C4×C11 |
| Hall | C11×C41 ⋊ Dic7 |
| Hall | C7×C11 ⋊ #4223 |
| Sylow | C41 ⋊ C11×Dic7 |
| Sylow | C7 ⋊ C11×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C7⋊#4223 |
| commutator, hypocenter | C7×C41 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C41 | C4 |
| prime radical | C7×C11×D41 | C2 |
| cosocle | C7×D41 | C2×C11 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
880 conjugacy classes — view the full character table.
| maximal subgroup of | C11×ΓL(1,𝔽8)⋊#4223, C3×C11×C7⋊#4223, C11×C3⋊(C7⋊#4223) |
| maximal normal subgroup of | C11×ΓL(1,𝔽8)⋊#4223, C3×C11×C7⋊#4223 |
| maximal quotient of | C3×C11×C7⋊#4223, C11×C3⋊(C7⋊#4223) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12628, 13);