Finite Group DatabasebetaFinite Group Databasebeta| order | 10556 |
| automorphism | Aut(G) order 10640448 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5278 |
| direct product | C2×D2639 |
| unambiguous semidirect product | (C2×C7)⋊D377 |
| unambiguous semidirect product | (C2×C13)⋊D203 |
| unambiguous semidirect product | (C2×C29)⋊D91 |
| Fitting, socle | C2×C7×C13×C29 ⋊ C2 |
| derived, Hall | C7×C13×C29 ⋊ C22 |
| Hall | C13×C29 ⋊ C2×D7 |
| Hall | C7×C29 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D91 |
| Sylow | C13 ⋊ C2×D203 |
| Sylow | C7 ⋊ C2×D377 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2639 |
| commutator, cosocle, hypocenter | C7×C13×C29 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13×C29 | C2 |
| LCS | G ▷ C7×C13×C29 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10556, 44);