Finite Group DatabasebetaFinite Group Databasebeta| order | 10556 |
| isoclinism | isoclinic class of D91 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×Dic91 |
| unambiguous semidirect product | C7⋊(C29×Dic13) |
| derived, Hall | C7×C13 ⋊ C4×C29 |
| Hall | C7×C13×C29 ⋊ C4 |
| Hall | C13×C29 ⋊ Dic7 |
| Hall | C7×C29 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic7×C29 |
| Sylow | C7 ⋊ C29×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D91 |
| commutator, hypocenter | C7×C13 | C4×C29 |
| Frattini | C2 | C29×D91 |
| Fitting, socle, prime radical | C2×C7×C13×C29 | C2 |
| cosocle | C2×C7×C13 | C2×C29 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C2×C29 | |
24 conjugacy classes of subgroups.
2726 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C29×Dic91, C29×Dic273, C29×#11763955, … |
| maximal normal subgroup of | C3×C29×Dic91, C29×#11763955, C29×ΓL(1,𝔽8)⋊Dic13, … |
| maximal quotient of | C3×C29×Dic91, C29×Dic273 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10556, 8);