Finite Group DatabasebetaFinite Group Databasebeta| order | 3556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D127 |
| unambiguous semidirect product | (D7×C127)⋊C2 |
| unambiguous semidirect product | (C7×D127)⋊C2 |
| unambiguous semidirect product | D889⋊C2 |
| Fitting, socle, derived, Hall | C7×C127 ⋊ C22 |
| Sylow | C127 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C127 | C22 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 134 |
| transitive degree | μt(G) = 889 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D7×D127, D35×D127, D7×D635, … |
| maximal normal subgroup of | C5×D7×D127, D7×D127⋊C7, C7×D7×D127 |
| maximal quotient of | C5×D7×D127, D35×D127, D7×D635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3556, 10);