Finite Group DatabasebetaFinite Group Databasebeta| order | 3556 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C4×C127⋊C7 |
| unambiguous semidirect product | (C4×C127)⋊C7 |
| Fitting, Hall | C4×C127 ⋊ C7 |
| derived, Sylow | C127 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C127⋊C7 |
| commutator, hypocenter | C127 | C4×C7 |
| Frattini | C2 | C2×C127⋊C7 |
| Fitting | C4×C127 | C7 |
| socle, cosocle | C2×C127 | C2×C7 |
| prime radical | C2×C127⋊C7 | C2 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 508 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C5×C127⋊C7, Dic5×C127⋊C7, AGL(1,𝔽5)×C127⋊C7, … |
| maximal normal subgroup of | C4×C5×C127⋊C7, C4×C7×C127⋊C7 |
| maximal quotient of | C4×C5×C127⋊C7, Dic5×C127⋊C7, AGL(1,𝔽5)×C127⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3556, 3);