Finite Group DatabasebetaFinite Group Databasebeta| order | 11765 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C181⋊C5 |
| unambiguous semidirect product | C181⋊(C5×C13) |
| unambiguous semidirect product | (C13×C181)⋊C5 |
| Fitting, socle, Hall | C13×C181 ⋊ C5 |
| derived, Sylow | C181 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C181⋊C5 |
| commutator, cosocle, hypocenter | C181 | C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C181 | C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
533 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13×C181⋊C5, C13×D181⋊C5, D13×C181⋊C5, … |
| maximal normal subgroup of | C2×C13×C181⋊C5, C13×D181⋊C5, D13×C181⋊C5, … |
| maximal quotient of | C2×C13×C181⋊C5, C3×C13×C181⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11765, 1);