Finite Group DatabasebetaFinite Group Databasebeta| order | 11935 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#13133721 |
| Fitting, socle, Hall | C7×C11×C31 ⋊ C5 |
| derived, Hall | C11×C31 ⋊ C5×C7 |
| Hall | C7×C31 ⋊ C11⋊C5 |
| Hall | C7×C11 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C7×C11⋊C5 |
| Sylow | C11 ⋊ C7×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13133721 |
| commutator, cosocle, hypocenter | C11×C31 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C31 | C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
511 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C7×#13133721, C7×#16811771, C7×#16811777, … |
| maximal normal subgroup of | C2×C7×#13133721, C7×#16811771, C7×#16811777, … |
| maximal quotient of | C2×C7×#13133721, C3×C7×#13133721 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11935, 4);