Finite Group DatabasebetaFinite Group Databasebeta| order | 16156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D577 |
| unambiguous semidirect product | (D7×C577)⋊C2 |
| unambiguous semidirect product | (C7×D577)⋊C2 |
| unambiguous semidirect product | D4039⋊C2 |
| Fitting, socle, derived, Hall | C7×C577 ⋊ C22 |
| Sylow | C577 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D577 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C577 | C22 |
| LCS | G ▷ C7×C577 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4039 |
1450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16156, 8);