Finite Group DatabasebetaFinite Group Databasebeta| order | 10556 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic29⋊C7 |
| unambiguous semidirect product | Dic29⋊(C7×C13) |
| unambiguous semidirect product | (C13×Dic29)⋊C7 |
| derived, Sylow | C29 ⋊ C4×C7×C13 |
| Hall | C13×C29⋊C7 ⋊ C4 |
| Hall | C13×Dic29 ⋊ C7 |
| Hall | C13×C29 ⋊ C4×C7 |
| Hall | C29⋊C7 ⋊ C4×C13 |
| Hall | Dic29 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D29⋊C7 |
| commutator, hypocenter | C29 | C4×C7×C13 |
| Frattini | C2 | C13×D29⋊C7 |
| Fitting, socle | C2×C13×C29 | C2×C7 |
| prime radical | C2×C13×C29⋊C7 | C2 |
| cosocle | C2×C29 | C2×C7×C13 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
416 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C13×Dic29⋊C7, C13×C3⋊(Dic29⋊C7), C13⋊C3×Dic29⋊C7 |
| maximal normal subgroup of | C3×C13×Dic29⋊C7, C13⋊C3×Dic29⋊C7 |
| maximal quotient of | C3×C13×Dic29⋊C7, C13×C3⋊(Dic29⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10556, 10);