Finite Group DatabasebetaFinite Group Databasebeta| order | 11739 |
| isoclinism | isoclinic class of #63270 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#63270 |
| Fitting, socle, Hall | C7×C13×C43 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C3×C43 |
| Hall | C13×C43 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C43 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C43 |
| Sylow | C7 ⋊ C13⋊C3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #63270 |
| commutator, cosocle, hypocenter | C7×C13 | C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C43 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
1419 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×#63270, D43×#63270, C43×#10587716, … |
| maximal normal subgroup of | C2×C43×#63270, D43×#63270, C43×#10587716, … |
| maximal quotient of | C2×C43×#63270, C43×#11717941, C3×C43×#63270 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11739, 10);