Finite Group DatabasebetaFinite Group Databasebeta| order | 10556 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic377⋊C7 |
| derived, Hall | C13×C29 ⋊ C4×C7 |
| Hall | C13×C29⋊C7 ⋊ C4 |
| Hall | Dic377 ⋊ C7 |
| Hall | C29⋊C7 ⋊ Dic13 |
| Sylow | C29 ⋊ C7×Dic13 |
| Sylow | C13 ⋊ Dic29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊(D29⋊C7) |
| commutator, hypocenter | C13×C29 | C4×C7 |
| Fitting, socle, cosocle | C2×C13×C29 | C2×C7 |
| prime radical | C2×C13×C29⋊C7 | C2 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,13,29,2|a^2=e,c^a=c^12,d^a=d^28,d^b=d^16164 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic377⋊C7, C3⋊(Dic377⋊C7), (Dic377⋊C3)⋊C7 |
| maximal normal subgroup of | C3×Dic377⋊C7, (Dic377⋊C3)⋊C7 |
| maximal quotient of | C3×Dic377⋊C7, C3⋊(Dic377⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10556, 12);