Finite Group DatabasebetaFinite Group Databasebeta| order | 11557 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C127⋊C7 |
| unambiguous semidirect product | C127⋊(C7×C13) |
| unambiguous semidirect product | (C13×C127)⋊C7 |
| Fitting, socle, Hall | C13×C127 ⋊ C7 |
| derived, Sylow | C127 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C127⋊C7 |
| commutator, cosocle, hypocenter | C127 | C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C127 | C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
325 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13×C127⋊C7, C13×D127⋊C7, D13×C127⋊C7, … |
| maximal normal subgroup of | C2×C13×C127⋊C7, C13×D127⋊C7, D13×C127⋊C7, … |
| maximal quotient of | C2×C13×C127⋊C7, C3×C13×C127⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11557, 1);