Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic43⋊C7 |
| unambiguous semidirect product | (C32×Dic43)⋊C7 |
| derived, Sylow | C43 ⋊ C32×C4×C7 |
| Hall | C32×C43⋊C7 ⋊ C4 |
| Hall | C32×Dic43 ⋊ C7 |
| Hall | C32×C43 ⋊ C4×C7 |
| Hall | C43⋊C7 ⋊ C32×C4 |
| Hall | Dic43 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D43⋊C7 |
| commutator, hypocenter | C43 | C32×C4×C7 |
| Frattini | C2 | C32×D43⋊C7 |
| Fitting, socle | C2×C32×C43 | C2×C7 |
| prime radical | C2×C32×C43⋊C7 | C2 |
| cosocle | C2×C43 | C2×C32×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
306 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 88);