Finite Group DatabasebetaFinite Group Databasebeta| order | 10556 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic377 |
| derived, Hall | C13×C29 ⋊ C4×C7 |
| Hall | C7×C13×C29 ⋊ C4 |
| Hall | C7×C29 ⋊ Dic13 |
| Hall | C7×C13 ⋊ Dic29 |
| Sylow | C29 ⋊ C7×Dic13 |
| Sylow | C13 ⋊ C7×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D377 |
| commutator, hypocenter | C13×C29 | C4×C7 |
| Frattini | C2 | C7×D377 |
| Fitting, socle, prime radical | C2×C7×C13×C29 | C2 |
| cosocle | C2×C13×C29 | C2×C7 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
2660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×Dic377, C7×Dic1131, C7×Dic377⋊C3, … |
| maximal normal subgroup of | C3×C7×Dic377, C7×Dic377⋊C3, ΓL(1,𝔽8)×Dic377, … |
| maximal quotient of | C3×C7×Dic377, C7×Dic1131 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10556, 5);